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GNU General Public License permit incorporating program proprietary programs. program subroutine library, may consider useful permit linking proprietary applications library. want , use GNU Lesser General Public License instead License. first, please read <http://www.gnu.org/philosophy/--lgpl.html>.","code":"<one line to give the program's name and a brief idea of what it does.> Copyright (C) <year>  <name of author>  This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.  This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.  You should have received a copy of the GNU General Public License along with this program.  If not, see <http://www.gnu.org/licenses/>. <program>  Copyright (C) <year>  <name of author> This program comes with ABSOLUTELY NO WARRANTY; for details type 'show w'. This is free software, and you are welcome to redistribute it under certain conditions; type 'show c' for details."},{"path":"https://lschneiderbauer.github.io/fCWTr/articles/sigma.html","id":"from-uncertainty-to-resolution","dir":"Articles","previous_headings":"","what":"From uncertainty to resolution","title":"Controlling the time/frequency resolution","text":"time frequency resolution \\(\\Delta t\\) \\(\\Delta f\\) can expect certain value \\(\\Sigma\\)? resolution set Gaussian spread turn quantified uncertainties \\(\\sigma_t\\) \\(\\sigma_f\\). Interpreting Gaussian window function, expect order achieve certain resolution \\(\\Delta_t\\) window size needs least equal (smaller) \\(\\Delta t\\). Since Gaussian infinite support, need make less arbitrary decision exponential falloff Gaussian close enough zero liking.  case, decide \\(4\\,\\sigma\\) effective width window function, expect effective resolution \\[\\Delta t:=\\frac{4Σ}{f}\\] \\[\\Delta f:=\\frac{2f}{πΣ}\\]","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/articles/sigma.html","id":"example-piano-keys","dir":"Articles","previous_headings":"","what":"Example: Piano keys","title":"Controlling the time/frequency resolution","text":"Let’s try understand meaning \\(\\Sigma\\) via example: like analyse piano music, able least distinguish different piano key frequencies. can, example, check resolutions corresponding \\(\\Sigma=1\\) key A4 (440 Hz) helper functions implement formulas : see now, \\(\\Sigma=1\\), frequency resolution 440 Hz 280 Hz! spreading way high able distinguish different keys (next key #4 466 Hz previous key Ab4 415 Hz), least need able resolve difference, 15 Hz. can use another helper function check corresponding \\(\\Sigma\\) : tells us need \\(\\Sigma=19\\) higher. Let’s double-check implies time resolution: means, can detect frequencies time resolution 170 milliseconds. typical fast piano beat around 180 beats per minutes (> Prestissimo), .e. three beats per seconds, required time resolution detect least 330 milliseconds: time resolution still , safe side.2 Let’s compare settings practice. example serves simple piano sample playing couple 440 Hz notes beginning simple chords end.","code":"library(fCWTr) sigma_res(sigma = 1, u(440, \"Hz\")) #> $time #> 0.009090909 [1/Hz] #>  #> $freq #> 280.1127 [Hz] sigma_from_freq_res(u(15, \"Hz\"), u(440, \"Hz\")) #> [1] 18.67418 sigma_res(sigma = 19, u(440, \"Hz\")) #> $time #> 0.1727273 [1/Hz] #>  #> $freq #> 14.74277 [Hz]"},{"path":"https://lschneiderbauer.github.io/fCWTr/articles/sigma.html","id":"high-time-resolution-low-frequency-resolution","dir":"Articles","previous_headings":"Example: Piano keys","what":"High time resolution, low frequency resolution","title":"Controlling the time/frequency resolution","text":"","code":"sigma_res(sigma = 1, u(440, \"Hz\")) #> $time #> 0.009090909 [1/Hz] #>  #> $freq #> 280.1127 [Hz] library(ggplot2)  fcwt(   ts_piano_sample,   x_sample_freq = u(44.1, \"kHz\") / 4,   sigma = 1,   y_sample_freq = u(10, \"Hz\"),   freq_begin = u(220, \"Hz\"),   freq_end = u(440, \"Hz\") * 4,   n_freqs = 12 * 5 * 3 ) |>   plot()"},{"path":"https://lschneiderbauer.github.io/fCWTr/articles/sigma.html","id":"good-middle-ground","dir":"Articles","previous_headings":"Example: Piano keys","what":"Good middle ground","title":"Controlling the time/frequency resolution","text":"","code":"sigma_res(sigma = 19, u(440, \"Hz\")) #> $time #> 0.1727273 [1/Hz] #>  #> $freq #> 14.74277 [Hz] fcwt(   ts_piano_sample,   x_sample_freq = u(44.1, \"kHz\") / 4,   sigma = 20,   y_sample_freq = u(10, \"Hz\"),   freq_begin = u(220, \"Hz\"),   freq_end = u(440, \"Hz\") * 4,   n_freqs = 12 * 5 * 3 ) |>   plot()"},{"path":"https://lschneiderbauer.github.io/fCWTr/articles/sigma.html","id":"low-time-resolution-high-frequency-resolution","dir":"Articles","previous_headings":"Example: Piano keys","what":"Low time resolution, high frequency resolution","title":"Controlling the time/frequency resolution","text":"Note \\(\\Sigma=100\\) barely time resolution one second. can see, can resolve beats second 12 18 anymore:  way, \\(\\Sigma\\) can thought exposure time camera adjusted manually. exposure time long picture becomes blurry; short, picture becomes dark see anything. good balance key good photo.","code":"sigma_res(sigma = 100, u(440, \"Hz\")) #> $time #> 0.9090909 [1/Hz] #>  #> $freq #> 2.801127 [Hz] fcwt(   ts_piano_sample,   x_sample_freq = u(44.1, \"kHz\") / 4,   sigma = 100,   y_sample_freq = u(10, \"Hz\"),   freq_begin = u(220, \"Hz\"),   freq_end = u(440, \"Hz\") * 4,   n_freqs = 12 * 5 * 3 ) |>   plot()"},{"path":"https://lschneiderbauer.github.io/fCWTr/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Lukas Schneiderbauer. Author, maintainer, copyright holder. Lukas P. . Arts. Copyright holder.           Author majority C++ code, indicated respective header files. Egon L. van den Broek. Copyright holder.           Author majority C++ code, indicated respective header files.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Schneiderbauer L (2025). fCWTr: Fast Continuous Wavelet Transform. R package version 0.3.1, https://github.com/lschneiderbauer/fCWTr, https://lschneiderbauer.github.io/fCWTr/.","code":"@Manual{,   title = {fCWTr: Fast Continuous Wavelet Transform},   author = {Lukas Schneiderbauer},   year = {2025},   note = {R package version 0.3.1, https://github.com/lschneiderbauer/fCWTr},   url = {https://lschneiderbauer.github.io/fCWTr/}, }"},{"path":"https://lschneiderbauer.github.io/fCWTr/index.html","id":"fcwtr-","dir":"","previous_headings":"","what":"Fast Continuous Wavelet Transform","title":"Fast Continuous Wavelet Transform","text":"R package fCWTr wraps fCWT library, library implementing continuous wavelet transform Morlet wavelet, utilizing power fftw, fast fourier transform implementation. provides R-like functional interface implements common S3 methods convenience. See original paper Arts, L.P.., van den Broek, E.L. fast continuous wavelet transformation (fCWT) real-time, high-quality, noise-resistant time–frequency analysis. Nat Comput Sci 2, 47–58 (2022). https://doi.org/10.1038/s43588-021-00183-z","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/index.html","id":"system-dependencies","dir":"","previous_headings":"","what":"System dependencies","title":"Fast Continuous Wavelet Transform","text":"R >= 4.1 fftw library single-precision support enabled (used fCWT) Optional: CPU/compiler supporting AVX instruction set Windows, OpenMP support disabled since rtools’ fftw compiled without OpenMP support. Linux MacOS build scripts automatically detect whether OpenMP support available. default, compiler setups make use AVX increase portability binary. R user CPU supporting AVX want make use , might need manually enable compiler flags let R know , install package source (gets compiled machine). One way enable flags create file ~/.R/Makevars following content:","code":"CPPFLAGS = -mavx CXXFLAGS = -mavx"},{"path":"https://lschneiderbauer.github.io/fCWTr/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Fast Continuous Wavelet Transform","text":"can install latest CRAN release fCWTr : Alternatively, can install development version fCWTr like (requiring installed devtools package): Note installation process might fail package needs compiled source system requirements satisfied. error message give hints, however, ’s missing system. Common confusion: fftw installed, compiled without single precision support. Please consult fftw.org help.","code":"install.packages(\"fCWTr\") devtools::install_github(\"lschneiderbauer/fCWTr\")"},{"path":"https://lschneiderbauer.github.io/fCWTr/index.html","id":"example","dir":"","previous_headings":"","what":"Example","title":"Fast Continuous Wavelet Transform","text":"basic example continuous wavelet transform sample signal calculated. result inspected plotted. result can also converted data frame: can also directly plot resulting scalogram:  long sequences, required memory can exceed available local memory. case can useful reduce time resolution result process data batches. can done fcwt_batch(). case batch size explicitly provided, heuristics used determine batch size automatically:","code":"library(fCWTr)  # A signal encoded in a numeric vector. # In this example we use some superimposed sin signals. signal <- ts_sin_superpos  output <-   fcwt(     signal,     x_sample_freq = u(44.1, \"kHz\"),     sigma = 5,     y_sample_freq = u(1, \"kHz\"),     freq_begin = u(16, \"Hz\"),     freq_end = u(2100, \"Hz\"),     n_freqs = 200,     freq_scale = \"linear\"   )  # The result is a numeric matrix with time and frequency dimension dim(output) #> [1] 137 200  # Some meta data is recorded too output #> _Scalogram_ #> * (Time/Frequency) dimension:  ( 137 , 200 ) #> * Sampling rate: 1 [kHz] #> * Frequency scale: 16 [Hz] - 2100 [Hz], linear #> * Time offset: 0 [s]  #> * Sigma: 5 #>   o Time resolution at  16 [Hz] :  1.25 [1/Hz]  #>   o Time resolution at  2100 [Hz] :  0.00952381 [1/Hz]  #>   o Relative frequency resolution:  0.127324  #> * Time/frequency matrix summary #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's  #>   0.000   0.000   0.000   0.003   0.001   0.064    6671 as.data.frame(output) |>   head(10) #>    time_index      time      freq        value #> 1           0 0.000 [s] 2100 [Hz]           NA #> 2           1 0.001 [s] 2100 [Hz]           NA #> 3           2 0.002 [s] 2100 [Hz]           NA #> 4           3 0.003 [s] 2100 [Hz]           NA #> 5           4 0.004 [s] 2100 [Hz] 5.170488e-05 #> 6           5 0.005 [s] 2100 [Hz] 2.023599e-05 #> 7           6 0.006 [s] 2100 [Hz] 7.007858e-06 #> 8           7 0.007 [s] 2100 [Hz] 2.413503e-06 #> 9           8 0.008 [s] 2100 [Hz] 1.058135e-06 #> 10          9 0.009 [s] 2100 [Hz] 6.853825e-07 plot(output, time_unit = \"ms\") batch_result <-   fcwt_batch(     rep(ts_sin_sin, 5),     x_sample_freq = u(44.1, \"kHz\"),     y_sample_freq = u(100, \"Hz\"),     freq_begin = u(100, \"Hz\"),     freq_end = u(12, \"kHz\"),     n_freqs = 200,     freq_scale = \"linear\",     sigma = 4   )  plot(batch_result)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.data.frame.fcwtr_scalogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert the scalogram matrix to a data frame — as.data.frame.fcwtr_scalogram","title":"Convert the scalogram matrix to a data frame — as.data.frame.fcwtr_scalogram","text":"Internally, scalogram resulting fcwt() represented numeric matrix(). method converts matrix three-columned data.frame() (two columns represent matrix indices, one column corresponding value). Note conversion significant run time cost.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.data.frame.fcwtr_scalogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert the scalogram matrix to a data frame — as.data.frame.fcwtr_scalogram","text":"","code":"# S3 method for class 'fcwtr_scalogram' as.data.frame(x, ...)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.data.frame.fcwtr_scalogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert the scalogram matrix to a data frame — as.data.frame.fcwtr_scalogram","text":"x \"fcwtr_scalogram\" object resulting fcwt(). ... Additional arguments ignored.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.data.frame.fcwtr_scalogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert the scalogram matrix to a data frame — as.data.frame.fcwtr_scalogram","text":"data.frame() object representing scalogram data four columns: time_index integer index uniquely identifying time slices. time time difference first time slice physical units. time unit inverse frequency unit chosen user sample_freq argument fcwt(). freq frequency units sample_freq argument fcwt(). value fCWT result particular time-frequency combination.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.data.frame.fcwtr_scalogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert the scalogram matrix to a data frame — as.data.frame.fcwtr_scalogram","text":"","code":"fcwt(   sin((1:5000) * 2 * pi * 440 / 44100),   x_sample_freq = u(44100, \"Hz\"),   n_freqs = 10 ) |>   as.data.frame() |>   head() #>   time_index             time       freq        value #> 1          0 0.0000000000 [s] 22050 [Hz]           NA #> 2          1 0.0003799356 [s] 22050 [Hz] 1.229610e-05 #> 3          2 0.0007598712 [s] 22050 [Hz] 7.816250e-06 #> 4          3 0.0011398069 [s] 22050 [Hz] 6.032826e-06 #> 5          4 0.0015197425 [s] 22050 [Hz] 5.094111e-06 #> 6          5 0.0018996781 [s] 22050 [Hz] 4.511332e-06"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.matrix.fcwtr_scalogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract the data matrix from a scalogram — as.matrix.fcwtr_scalogram","title":"Extract the data matrix from a scalogram — as.matrix.fcwtr_scalogram","text":"Strips attributes class scalogram object retrieve pure matrix.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.matrix.fcwtr_scalogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract the data matrix from a scalogram — as.matrix.fcwtr_scalogram","text":"","code":"# S3 method for class 'fcwtr_scalogram' as.matrix(x, ...)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.matrix.fcwtr_scalogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract the data matrix from a scalogram — as.matrix.fcwtr_scalogram","text":"x \"fcwtr_scalogram\" object resulting fcwt(). ... additional arguments passed methods.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.matrix.fcwtr_scalogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extract the data matrix from a scalogram — as.matrix.fcwtr_scalogram","text":"two dimensional numeric vector, inheriting class \"matrix\".","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as.matrix.fcwtr_scalogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Extract the data matrix from a scalogram — as.matrix.fcwtr_scalogram","text":"","code":"options(max.print = 10)  fcwt(   sin((1:5000) * 2 * pi * 440 / 44100),   x_sample_freq = u(44100, \"Hz\"),   n_freqs = 10 ) |>   as.matrix() #>                [,1]         [,2]         [,3]         [,4]         [,5] #>   [1,]           NA           NA           NA           NA           NA #>               [,6] [,7] [,8] [,9] [,10] #>   [1,]          NA   NA   NA   NA    NA #>  [ reached getOption(\"max.print\") -- omitted 312 rows ]"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as_tibble.fcwtr_scalogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert the scalogram matrix to a tibble — as_tibble.fcwtr_scalogram","title":"Convert the scalogram matrix to a tibble — as_tibble.fcwtr_scalogram","text":"Internally, scalogram resulting fcwt() represented numeric matrix(). method converts matrix three-columned tibble::tibble() (two columns represent matrix indices, one column corresponding value). Note conversion significant run time cost.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as_tibble.fcwtr_scalogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert the scalogram matrix to a tibble — as_tibble.fcwtr_scalogram","text":"","code":"# S3 method for class 'fcwtr_scalogram' as_tibble(x, ...)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as_tibble.fcwtr_scalogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert the scalogram matrix to a tibble — as_tibble.fcwtr_scalogram","text":"x \"fcwtr_scalogram\" object resulting fcwt(). ... Additional arguments ignored.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as_tibble.fcwtr_scalogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert the scalogram matrix to a tibble — as_tibble.fcwtr_scalogram","text":"tibble::tibble() object representing scalogram data four columns: time_index integer index uniquely identifying time slices. time time difference first time slice physical units. time unit inverse frequency unit chosen user sample_freq argument fcwt(). freq frequency units sample_freq argument fcwt(). value fCWT result particular time-frequency combination.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as_tibble.fcwtr_scalogram.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Convert the scalogram matrix to a tibble — as_tibble.fcwtr_scalogram","text":"method conceptually identical .data.frame(), simply returns tibble::tibble() instead data.frame().","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/as_tibble.fcwtr_scalogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert the scalogram matrix to a tibble — as_tibble.fcwtr_scalogram","text":"","code":"library(tibble)  fcwt(   sin((1:5000) * 2 * pi * 440 / 44100),   x_sample_freq = u(44100, \"Hz\"),   n_freqs = 10 ) |>   as_tibble() #> # A tibble: 3,130 × 4 #>    time_index     time   freq       value #>         <dbl>      [s]   [Hz]       <dbl> #>  1          0 0        22050. NA          #>  2          1 0.000380 22050.  0.0000123  #>  3          2 0.000760 22050.  0.00000782 #>  4          3 0.00114  22050.  0.00000603 #>  5          4 0.00152  22050.  0.00000509 #>  6          5 0.00190  22050.  0.00000451 #>  7          6 0.00228  22050.  0.00000412 #>  8          7 0.00266  22050.  0.00000383 #>  9          8 0.00304  22050.  0.00000362 #> 10          9 0.00342  22050.  0.00000346 #> # ℹ 3,120 more rows"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/autoplot.fcwtr_scalogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a ggplot object resembling a scalogram — autoplot.fcwtr_scalogram","title":"Create a ggplot object resembling a scalogram — autoplot.fcwtr_scalogram","text":"Create ggplot object resembling scalogram","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/autoplot.fcwtr_scalogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a ggplot object resembling a scalogram — autoplot.fcwtr_scalogram","text":"","code":"# S3 method for class 'fcwtr_scalogram' autoplot(   object,   n = 1000,   time_unit = \"s\",   freq_unit = \"Hz\",   transf = identity,   ... )"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/autoplot.fcwtr_scalogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a ggplot object resembling a scalogram — autoplot.fcwtr_scalogram","text":"object \"fcwtr_scalogram\" object resulting fcwt(). n plotting function reduces time resolution averaging generate reasonable graphics format. n number time steps plotted. Defaults n = 1000. time_unit time unit used x-axis scale. Default \"s\" - seconds. See units::valid_udunits() units::valid_udunits_prefixes() valid expressions. freq_unit frequency unit used y-axis scale. Defaults \"Hz\" - \"Hertz\". See units::valid_udunits() units::valid_udunits_prefixes() valid expressions. transf function, taking vector returning vector, used transform scalogram values plotting. ... arguments passed specific methods","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/autoplot.fcwtr_scalogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a ggplot object resembling a scalogram — autoplot.fcwtr_scalogram","text":"ggplot object.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/autoplot.fcwtr_scalogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a ggplot object resembling a scalogram — autoplot.fcwtr_scalogram","text":"","code":"library(ggplot2)  res <-   fcwt(     sin((1:4410) * 2 * pi * 440 / 44100),     x_sample_freq = u(44100, \"Hz\"),     freq_begin = u(50, \"Hz\"),     freq_end = u(1000, \"Hz\"),     n_freqs = 10,     sigma = 5   )  autoplot(res, time_unit = \"ms\")"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/avx_enabled.html","id":null,"dir":"Reference","previous_headings":"","what":"Check for AVX instruction set support — avx_enabled","title":"Check for AVX instruction set support — avx_enabled","text":"function checks fCWTr compiled AVX instruction set support. AVX instructions need supported users' CPU order work.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/avx_enabled.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check for AVX instruction set support — avx_enabled","text":"","code":"avx_enabled()"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/avx_enabled.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check for AVX instruction set support — avx_enabled","text":"( TRUE | FALSE ) Returns TRUE AVX support enabled, FALSE otherwise.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/avx_enabled.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Check for AVX instruction set support — avx_enabled","text":"default, compiler setups make use AVX increase portability binary. R user CPU supporting AVX want make use , might need manually enable compiler flags let R know , install package source (gets compiled machine).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/avx_enabled.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Check for AVX instruction set support — avx_enabled","text":"","code":"avx_enabled() #> [1] FALSE"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/du.html","id":null,"dir":"Reference","previous_headings":"","what":"Drop physical unit — du","title":"Drop physical unit — du","text":"Drop units dimensionful quantity retrieve dimensionless number. dimensionless number defined ratio x one unit u(1, unit).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/du.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Drop physical unit — du","text":"","code":"du(x, unit = \"1\")"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/du.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Drop physical unit — du","text":"x dimensionful numeric vector (S3 class \"units\"), e.g. generated u() subsequent calculations. unit character indicating unit. See units::valid_udunits() units::valid_udunits_prefixes() possible units.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/du.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Drop physical unit — du","text":"dimensionless number defined ratio x one unit u(1, unit).","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/du.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Drop physical unit — du","text":"","code":"x <- u(1, \"km\")   # retrieve a dimensionless number  # from x in units of \"meter\"  du(x, \"m\") #> [1] 1000   # drop the unit of a dimensionaless \"unit\" quantity  du(x / x) #> [1] 1"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt.html","id":null,"dir":"Reference","previous_headings":"","what":"Fast continuous wavelet transform — fcwt","title":"Fast continuous wavelet transform — fcwt","text":"core function package making use fCWT library. processes input signal form real valued numeric vector interpreted evenly spaced time series returns absolute values continuous wavelet transform,  .e. real valued positive matrix time frequency dimension.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fast continuous wavelet transform — fcwt","text":"","code":"fcwt(   x,   x_sample_freq,   sigma = 2 * pi,   y_sample_freq = 3/sigma_res(sigma, freq_end)$time,   freq_begin = 2 * x_sample_freq/length(x),   freq_end = x_sample_freq/2,   n_freqs = 3 * ceiling(log(du(freq_end/freq_begin), base = 1 +     sigma_freq_res_rel(sigma))),   freq_scale = c(\"log\", \"linear\"),   rm_coi = TRUE,   n_threads = 2L )"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fast continuous wavelet transform — fcwt","text":"x Real-valued time series. time steps assumed evenly spaced. x_sample_freq Sampling rate input time series x. number primarily establishes connection physical units used frequency definitions well units output data. Expects either value frequency units, generated u(), pure number, case interpreted units 'Hertz'. sigma Sets dimensionless parameter \\(\\Sigma\\) controlling wavelet spread. Changing parameter adjusts time/frequency uncertainty balance, \\(\\Delta t = 4 \\frac{\\Sigma}{f}\\), \\(\\Delta f = 4 \\frac{f}{2\\pi \\Sigma}\\). Larger (lower) value sigma corresponds better (worse) frequency resolution worse (better) time resolution. information, see vignette(\"sigma\", package = \"fCWTr\")). Defaults \\(2\\pi\\). Note really natural choice sigma, depends use case. default choice can well quite bad choice (probably audio data). y_sample_freq Sampling rate output time series, frequency units (see u()). default value set aligns physical time resolution highest frequency modes. maximum allowed sampling rate sampling rate input signal x_sample_freq. freq_begin, freq_end Optionally specifies frequency range [freq_end, freq_begin]. specified maximal meaningful frequency range, depending input signal, taken. frequency-valued number, generated u(), pure number, interpreted units 'Hertz'. n_freqs Number frequency bins generated CWT. frequencies linearly logarithmically distributed, depending freq_scale argument. Computation time increases raising number frequency bins. default number chosen frequency bandwidths size physical frequency resolutions case logarithmic scale. sense value constitutes \"physical\" limit. However, increasing n_freqs beyond limit can still make sense: signal precise frequency, probing frequency band exactly aligned, output signal dampened. case can useful increase n_freqs perform appropriate averaging afterwards: output signal show improved response. freq_scale ( \"log\" | \"linear\" ) frequency scale linear logarithmic? \"linear\"  / \"log\" linear / logarithmic. default scale logarithmic since differences logarithmic scale proportional frequency uncertainties. sense, logarithmic frequency scale actually natural scale continuous wavelet transform. rm_coi ( TRUE | FALSE ) Boundary effects can result nonphysical artifacts. rm_coi = TRUE, effectively removed setting corresponding values NA. define essential support (Gaussian) wavelet four times standard deviation, \\(\\Delta t = \\frac{\\sigma}{f}\\), wavelet touches boundary distance center wavelet boundary less \\(\\Delta t /2\\). Values fall range removed rm_coi = TRUE. n_threads Number threads used computation, supported platform. Defaults 2 threads (accommodate CRAN requirements). openmp_enabled() returns FALSE, argument ignored, single thread used.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fast continuous wavelet transform — fcwt","text":"spectogram, numeric real-valued matrix dimensions dim = c(length(x), n_freqs), curated additional properties. matrix wrapped S3-class fcwtr_scalogram plotting coercion functions can used conveniently. Use .matrix() strip curated information. use .data.frame() convert another data format.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fast continuous wavelet transform — fcwt","text":"wavelet used calculation called Morlet wavelet, sinusoidal wave modulated Gaussian whose spread controlled argument sigma. See original paper Arts, L.P.., van den Broek, E.L. fast continuous wavelet transformation (fCWT) real-time, high-quality, noise-resistant time–frequency analysis. Nat Comput Sci 2, 47–58 (2022). doi:10.1038/s43588-021-00183-z","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fast continuous wavelet transform — fcwt","text":"","code":"ts_sin_440 <- sin((1:5000) * 2 * pi * 440 / 44100)  fcwt(   ts_sin_440,   x_sample_freq = u(44.1, \"kHz\"),   sigma = 5,   freq_begin = u(50, \"Hz\"),   freq_end = u(1000, \"Hz\"),   n_freqs = 10 ) #> _Scalogram_ #> * (Time/Frequency) dimension:  ( 18 , 10 ) #> * Sampling rate: 150 [Hz] #> * Frequency scale: 50 [Hz] - 1000 [Hz], log #> * Time offset: 0 [s]  #> * Sigma: 5 #>   o Time resolution at  50 [Hz] :  0.4 [1/Hz]  #>   o Time resolution at  1000 [Hz] :  0.02 [1/Hz]  #>   o Relative frequency resolution:  0.127324  #> * Time/frequency matrix summary #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's  #> 0.00000 0.00000 0.00000 0.00001 0.00001 0.00023     114"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt_batch.html","id":null,"dir":"Reference","previous_headings":"","what":"Fast continuous wavelet transform - Batch processing — fcwt_batch","title":"Fast continuous wavelet transform - Batch processing — fcwt_batch","text":"Performs fast continuous wavelet transform long sequences sequentially processing junks input signal keeping low-resolution output data averaging preserve memory. useful long signals whose output fit available memory whole. used short signals since boundary artefacts automatically discarded (potentially dominate short signals).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt_batch.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fast continuous wavelet transform - Batch processing — fcwt_batch","text":"","code":"fcwt_batch(   x,   x_sample_freq,   sigma = 1,   y_sample_freq = 3/sigma_res(sigma, freq_end)$time,   freq_begin = 2 * x_sample_freq/length(x),   freq_end = x_sample_freq/2,   n_freqs = 2 * ceiling(log(du(freq_end/freq_begin), base = 1 +     sigma_freq_res_rel(sigma))),   freq_scale = c(\"log\", \"linear\"),   max_batch_size = ceiling(1 * 10^9/(n_freqs * 8)/2),   n_threads = 2L,   progress_bar = FALSE )"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt_batch.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fast continuous wavelet transform - Batch processing — fcwt_batch","text":"x Real-valued time series. time steps assumed evenly spaced. x_sample_freq Sampling rate input time series x. number primarily establishes connection physical units used frequency definitions well units output data. Expects either value frequency units, generated u(), pure number, case interpreted units 'Hertz'. sigma Sets dimensionless parameter \\(\\Sigma\\) controlling wavelet spread. Changing parameter adjusts time/frequency uncertainty balance, \\(\\Delta t = 4 \\frac{\\Sigma}{f}\\), \\(\\Delta f = 4 \\frac{f}{2\\pi \\Sigma}\\). Larger (lower) value sigma corresponds better (worse) frequency resolution worse (better) time resolution. information, see vignette(\"sigma\", package = \"fCWTr\")). Defaults \\(2\\pi\\). Note really natural choice sigma, depends use case. default choice can well quite bad choice (probably audio data). y_sample_freq Sampling rate output time series, frequency units (see u()). default value set aligns physical time resolution highest frequency modes. maximum allowed sampling rate sampling rate input signal x_sample_freq. freq_begin, freq_end Optionally specifies frequency range [freq_end, freq_begin]. specified maximal meaningful frequency range, depending input signal, taken. frequency-valued number, generated u(), pure number, interpreted units 'Hertz'. n_freqs Number frequency bins generated CWT. frequencies linearly logarithmically distributed, depending freq_scale argument. Computation time increases raising number frequency bins. default number chosen frequency bandwidths size physical frequency resolutions case logarithmic scale. sense value constitutes \"physical\" limit. However, increasing n_freqs beyond limit can still make sense: signal precise frequency, probing frequency band exactly aligned, output signal dampened. case can useful increase n_freqs perform appropriate averaging afterwards: output signal show improved response. freq_scale ( \"log\" | \"linear\" ) frequency scale linear logarithmic? \"linear\"  / \"log\" linear / logarithmic. default scale logarithmic since differences logarithmic scale proportional frequency uncertainties. sense, logarithmic frequency scale actually natural scale continuous wavelet transform. max_batch_size maximal batch size used splitting input sequence. limits maximal memory used. Defaults roughly 1GB, conservative taking account R might make copies processing . actual batch size largest batch size smaller max_batch_size compatible requested y_sample_freq. aim set batch size large possible given memory constraints (boundary effects become larger smaller batch size). n_threads Number threads used computation, supported platform. Defaults 2 threads (accommodate CRAN requirements). openmp_enabled() returns FALSE, argument ignored, single thread used. progress_bar Monitoring progress can sometimes useful performing time consuming operations. Setting progress_bar = TRUE enables printing progress bar console, printing \"loss ratio\" number batches. loss ratio number 0 1 indicates much batch computation thrown away due boundary artefacts. higher batch size smaller loss ratio . Defaults FALSE.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt_batch.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fast continuous wavelet transform - Batch processing — fcwt_batch","text":"spectogram, numeric real-valued matrix dimensions roughly dim ~ c(length(x) * x_sample_freq / y_sample_freq, n_freqs). exact length output depends boundary effect details. matrix wrapped S3-class \"fcwtr_scalogram\" plotting coercion functions can used conveniently.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt_batch.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fast continuous wavelet transform - Batch processing — fcwt_batch","text":"case input sequences exceed certain size, output sequence fit local memory fcwt performed one run. instance, case processing song 10 minutes length (assuming sampling rate 44100 Hz), size output vector 10 * 60 seconds * 44100 Hz * nfreqs * 8 bytes, e.g. nfreqs = 200, equals ~ 42 GB, hence nowadays already limit hardware modern personal computer. cases required output time-resolution smaller time resolution input signal, one can perform fcwt() reduce output size averaging. (input signal time resolution can general reduced since high-frequency information get lost.) function splits input sequence batches, processes batch separately, reduces time resolution, adds outputs together. Attention: contrast fcwt() boundary artefacts automatically removed, information beginning end sequence lost. (amount depends minimal frequency captured min_freq.)","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/fcwt_batch.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fast continuous wavelet transform - Batch processing — fcwt_batch","text":"","code":"fcwt_batch(   ts_sin_sin,   x_sample_freq = u(44.1, \"kHz\"),   sigma = 10,   y_sample_freq = u(100, \"Hz\"),   freq_begin = u(100, \"Hz\"),   freq_end = u(11000, \"Hz\"),   n_freqs = 30 ) #> _Scalogram_ #> * (Time/Frequency) dimension:  ( 60 , 30 ) #> * Sampling rate: 100 [Hz] #> * Frequency scale: 100 [Hz] - 11000 [Hz], log #> * Time offset: 0.2 [s]  #> * Sigma: 10 #>   o Time resolution at  100 [Hz] :  0.4 [1/Hz]  #>   o Time resolution at  11000 [Hz] :  0.003636364 [1/Hz]  #>   o Relative frequency resolution:  0.06366198  #> * Time/frequency matrix summary #>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.  #> 0.000e+00 8.500e-09 1.850e-08 1.991e-05 4.640e-08 2.117e-03"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/openmp_enabled.html","id":null,"dir":"Reference","previous_headings":"","what":"Check for OpenMP support — openmp_enabled","title":"Check for OpenMP support — openmp_enabled","text":"function checks OpenMP support enabled. responsible multithreading capabilities fcwt(). OpenMP enabled parameter n_threads fcwt() ignored.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/openmp_enabled.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check for OpenMP support — openmp_enabled","text":"","code":"openmp_enabled()"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/openmp_enabled.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check for OpenMP support — openmp_enabled","text":"( TRUE | FALSE ) Returns TRUE OpenMP support enabled, FALSE otherwise.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/openmp_enabled.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Check for OpenMP support — openmp_enabled","text":"OpenMP can used underlying fCWT library fftw library platform compiled OpenMP support fCWTr package compiled OpenMP support. using pre-built package binaries (like typical using R Windows), depends (CRAN) build server whether conditions met. influenced package author. user building R package , user needs make sure fftw library platform built OpenMP support. fCWTr package configured use OpenMP fftw-OpenMP support available.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/openmp_enabled.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Check for OpenMP support — openmp_enabled","text":"","code":"openmp_enabled() #> [1] TRUE"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/plot.fcwtr_scalogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Scalogram plotting — plot.fcwtr_scalogram","title":"Scalogram plotting — plot.fcwtr_scalogram","text":"Plots scalogram resulting fcwt(). Requires ggplot2.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/plot.fcwtr_scalogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Scalogram plotting — plot.fcwtr_scalogram","text":"","code":"# S3 method for class 'fcwtr_scalogram' plot(x, n = 1000, time_unit = \"s\", freq_unit = \"Hz\", transf = identity, ...)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/plot.fcwtr_scalogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Scalogram plotting — plot.fcwtr_scalogram","text":"x \"fcwtr_scalogram\" object resulting fcwt(). n plotting function reduces time resolution averaging generate reasonable graphics format. n number time steps plotted. Defaults n = 1000. time_unit time unit used x-axis scale. Default \"s\" - seconds. See units::valid_udunits() units::valid_udunits_prefixes() valid expressions. freq_unit frequency unit used y-axis scale. Defaults \"Hz\" - \"Hertz\". See units::valid_udunits() units::valid_udunits_prefixes() valid expressions. transf function, taking vector returning vector, used transform scalogram values plotting. ... arguments passed specific methods","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/plot.fcwtr_scalogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Scalogram plotting — plot.fcwtr_scalogram","text":"return value, called side effects.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/plot.fcwtr_scalogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Scalogram plotting — plot.fcwtr_scalogram","text":"","code":"ts_sin_440 <- sin((1:4410) * 2 * pi * 440 / 44100)  res <-   fcwt(     ts_sin_440,     x_sample_freq = u(44100, \"Hz\"),     freq_begin = u(50, \"Hz\"),     freq_end = u(1000, \"Hz\"),     n_freqs = 10,     sigma = 5   )  plot(res, time_unit = \"ms\")"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/print.fcwtr_scalogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Print the scalogram — print.fcwtr_scalogram","title":"Print the scalogram — print.fcwtr_scalogram","text":"print() prints argument returns invisibly (via invisible(x)).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/print.fcwtr_scalogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print the scalogram — print.fcwtr_scalogram","text":"","code":"# S3 method for class 'fcwtr_scalogram' print(x, ...)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/print.fcwtr_scalogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print the scalogram — print.fcwtr_scalogram","text":"x \"fcwtr_scalogram\" object resulting fcwt() print. ... arguments passed methods.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/print.fcwtr_scalogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print the scalogram — print.fcwtr_scalogram","text":"Returns argument x invisibly.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/rbind.fcwtr_scalogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Combine scalograms in ","title":"Combine scalograms in ","text":"Given two scalograms identical sampling frequencies, frequency scales sigma, can useful combine several single object creating longer time series. function errs conditions satisfied.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/rbind.fcwtr_scalogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Combine scalograms in ","text":"","code":"# S3 method for class 'fcwtr_scalogram' rbind(...)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/rbind.fcwtr_scalogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Combine scalograms in ","text":"... One \"fcwtr_scalogram\" objects, generated fcwt().","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/rbind.fcwtr_scalogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Combine scalograms in ","text":"Returns new time-wise combined \"fcwtr_scalogram\" object.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/rbind.fcwtr_scalogram.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Combine scalograms in ","text":"scalograms stitched together chronological fashion (.e. first argument initial piece, etc.). Time offset information kept first piece.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/rbind.fcwtr_scalogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Combine scalograms in ","text":"","code":"ts_sin_440 <- sin((1:5000) * 2 * pi * 440 / 44100)  res <-   fcwt(     ts_sin_440,     x_sample_freq = u(44.1, \"kHz\"),     freq_begin = u(50, \"Hz\"),     freq_end = u(1000, \"Hz\"),     n_freqs = 10,     sigma = 5   )  print(res) #> _Scalogram_ #> * (Time/Frequency) dimension:  ( 18 , 10 ) #> * Sampling rate: 150 [Hz] #> * Frequency scale: 50 [Hz] - 1000 [Hz], log #> * Time offset: 0 [s]  #> * Sigma: 5 #>   o Time resolution at  50 [Hz] :  0.4 [1/Hz]  #>   o Time resolution at  1000 [Hz] :  0.02 [1/Hz]  #>   o Relative frequency resolution:  0.127324  #> * Time/frequency matrix summary #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's  #> 0.00000 0.00000 0.00000 0.00001 0.00001 0.00023     114   # doubled scalogram res_doubled <- rbind(res, res)  print(res_doubled) #> _Scalogram_ #> * (Time/Frequency) dimension:  ( 36 , 10 ) #> * Sampling rate: 150 [Hz] #> * Frequency scale: 50 [Hz] - 1000 [Hz], log #> * Time offset: 0 [s]  #> * Sigma: 5 #>   o Time resolution at  50 [Hz] :  0.4 [1/Hz]  #>   o Time resolution at  1000 [Hz] :  0.02 [1/Hz]  #>   o Relative frequency resolution:  0.127324  #> * Time/frequency matrix summary #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's  #> 0.00000 0.00000 0.00000 0.00001 0.00001 0.00023     228"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_freq_res_rel.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculates Relative Frequency Resolution — sigma_freq_res_rel","title":"Calculates Relative Frequency Resolution — sigma_freq_res_rel","text":"given sigma function calculates expected relative frequency resolution respectively.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_freq_res_rel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculates Relative Frequency Resolution — sigma_freq_res_rel","text":"","code":"sigma_freq_res_rel(sigma)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_freq_res_rel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculates Relative Frequency Resolution — sigma_freq_res_rel","text":"sigma dimensionless positive parameter fcwt() controlling wavelet spread.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_freq_res_rel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculates Relative Frequency Resolution — sigma_freq_res_rel","text":"number p representing relative frequency resolution. .e. given resolution f, frequency resolution f*p.","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_freq_res_rel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculates Relative Frequency Resolution — sigma_freq_res_rel","text":"","code":"sigma_freq_res_rel(1) #> [1] 0.6366198"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res.html","id":null,"dir":"Reference","previous_headings":"","what":"Determine Sigma from a frequency resolution requirement — sigma_from_freq_res","title":"Determine Sigma from a frequency resolution requirement — sigma_from_freq_res","text":"Setting correct value sigma fcwt() particular use case important. Sigma controls wavelet spread used FCWT determines time-/frequency resolution (depending given reference frequency).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Determine Sigma from a frequency resolution requirement — sigma_from_freq_res","text":"","code":"sigma_from_freq_res(res, freq)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Determine Sigma from a frequency resolution requirement — sigma_from_freq_res","text":"res required frequency resolution frequency units (see u()). freq reference frequency required resolution must hold. Must quantity frequency units (see u()).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Determine Sigma from a frequency resolution requirement — sigma_from_freq_res","text":"dimensionless number controlling FCWT wavelet spread, corresponding sigma argument fcwt().","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Determine Sigma from a frequency resolution requirement — sigma_from_freq_res","text":"set high frequency resolution, time resolution output signal suffer, vice versa. Determining correct balance particular use case can crucial. function determines value sigma particular frequency resolution requirement.","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Determine Sigma from a frequency resolution requirement — sigma_from_freq_res","text":"","code":"ref_freq <- u(440, \"Hz\") sigma <- sigma_from_freq_res(u(7, \"Hz\"), ref_freq)  sigma_res(sigma, ref_freq) #> $time #> 0.3637827 [1/Hz] #>  #> $freq #> 7 [Hz] #>"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res_rel.html","id":null,"dir":"Reference","previous_headings":"","what":"Determine Sigma from a relative frequency resolution requirement — sigma_from_freq_res_rel","title":"Determine Sigma from a relative frequency resolution requirement — sigma_from_freq_res_rel","text":"Setting correct value sigma fcwt() particular use case important. Sigma controls wavelet spread used FCWT determines time-/frequency resolution (depending given reference frequency).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res_rel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Determine Sigma from a relative frequency resolution requirement — sigma_from_freq_res_rel","text":"","code":"sigma_from_freq_res_rel(res)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res_rel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Determine Sigma from a relative frequency resolution requirement — sigma_from_freq_res_rel","text":"res required relative frequency resolution, number 0 1.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res_rel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Determine Sigma from a relative frequency resolution requirement — sigma_from_freq_res_rel","text":"dimensionless number controlling FCWT wavelet spread, corresponding sigma argument fcwt().","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res_rel.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Determine Sigma from a relative frequency resolution requirement — sigma_from_freq_res_rel","text":"set high frequency resolution, time resolution output signal suffer, vice versa. Determining correct balance particular use case can crucial. function determines value sigma particular relative frequency resolution requirement. Note relative frequency resolution depend frequency , contrast absolute frequency resolution.","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_freq_res_rel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Determine Sigma from a relative frequency resolution requirement — sigma_from_freq_res_rel","text":"","code":"ref_freq <- u(440, \"Hz\") sigma <- sigma_from_freq_res_rel(0.2)  sigma_res(sigma, ref_freq) #> $time #> 0.02893726 [1/Hz] #>  #> $freq #> 88 [Hz] #>"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_time_res.html","id":null,"dir":"Reference","previous_headings":"","what":"Determine Sigma from a time resolution requirement — sigma_from_time_res","title":"Determine Sigma from a time resolution requirement — sigma_from_time_res","text":"Setting correct value sigma fcwt() particular use case important. Sigma controls wavelet spread used FCWT determines time-/frequency resolution (depending given reference frequency).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_time_res.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Determine Sigma from a time resolution requirement — sigma_from_time_res","text":"","code":"sigma_from_time_res(res, freq)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_time_res.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Determine Sigma from a time resolution requirement — sigma_from_time_res","text":"res required time resolution frequency units (see u()). freq reference frequency required resolution must hold. Must quantity frequency units (see u()).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_time_res.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Determine Sigma from a time resolution requirement — sigma_from_time_res","text":"dimensionless number controlling FCWT wavelet spread, corresponding sigma argument fcwt().","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_time_res.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Determine Sigma from a time resolution requirement — sigma_from_time_res","text":"set high frequency resolution, time resolution output signal suffer, vice versa. Determining correct balance particular use case can crucial. function determines value sigma particular time resolution requirement.","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_from_time_res.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Determine Sigma from a time resolution requirement — sigma_from_time_res","text":"","code":"ref_freq <- u(440, \"Hz\") sigma <- sigma_from_time_res(u(10, \"ms\"), ref_freq)  sigma_res(sigma, ref_freq) #> $time #> 0.01 [1/Hz] #>  #> $freq #> 254.6479 [Hz] #>"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_res.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculates Time/Frequency Resolution — sigma_res","title":"Calculates Time/Frequency Resolution — sigma_res","text":"given sigma reference frequency freq function calculates expected time frequency resolution respectively.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_res.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculates Time/Frequency Resolution — sigma_res","text":"","code":"sigma_res(sigma, freq)"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_res.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculates Time/Frequency Resolution — sigma_res","text":"sigma dimensionless positive parameter fcwt() controlling wavelet spread. freq reference frequency frequency time resolution calculated. Must quantity frequency units (see u()).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_res.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculates Time/Frequency Resolution — sigma_res","text":"named list two elements: \"time\" \"freq\", time frequency units. obey property \\(time \\times freq = \\frac{8}{\\pi}\\).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_res.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculates Time/Frequency Resolution — sigma_res","text":"Note resolution depends reference frequency, since FCWT scales wavelet spread depending frequency natural way. (contrast simple fixed-windowed Fourier Transform).","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sigma_res.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculates Time/Frequency Resolution — sigma_res","text":"","code":"sigma_res(1, u(440, \"Hz\")) #> $time #> 0.009090909 [1/Hz] #>  #> $freq #> 280.1127 [Hz] #>"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sub-.fcwtr_scalogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract parts of a scalogram — [.fcwtr_scalogram","title":"Extract parts of a scalogram — [.fcwtr_scalogram","text":"Extract parts scalogram","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sub-.fcwtr_scalogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract parts of a scalogram — [.fcwtr_scalogram","text":"","code":"# S3 method for class 'fcwtr_scalogram' x[i, j]"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sub-.fcwtr_scalogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract parts of a scalogram — [.fcwtr_scalogram","text":"x \"fcwtr_scalogram\" object resulting fcwt(). , j Indices corresponding time slices spectogram specify elements extract. Indices numeric vectors empty (missing) NULL. Numeric values coerced integer whole numbers .integer large values trunc() (hence truncated towards zero). time offset scalogram adjusted correspond min(). [-indexing : , j, ... can logical vectors, indicating elements/slices select. vectors recycled necessary match corresponding extent. , j, ... can also negative integers, indicating elements/slices leave selection. indexing arrays [ single argument can matrix many columns dimensions x; result vector elements corresponding sets indices row . index value NULL treated integer(0).","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sub-.fcwtr_scalogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extract parts of a scalogram — [.fcwtr_scalogram","text":"Another \"fcwtr_scalogram\" object contains part data.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/sub-.fcwtr_scalogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Extract parts of a scalogram — [.fcwtr_scalogram","text":"","code":"fcwt(   sin((1:5000) * 2 * pi * 440 / 44100),   x_sample_freq = u(44100, \"Hz\"),   y_sample_freq = u(44100, \"Hz\"),   n_freqs = 10 )[1:1000, 2:7] #> _Scalogram_ #> * (Time/Frequency) dimension:  ( 1000 , 6 ) #> * Sampling rate: 44100 [Hz] #> * Frequency scale: 17.64 [Hz] - 22050 [Hz], log #> * Time offset: 0 [s]  #> * Sigma: 6.283185 #>   o Time resolution at  17.64 [Hz] :  1.424759 [1/Hz]  #>   o Time resolution at  22050 [Hz] :  0.001139807 [1/Hz]  #>   o Relative frequency resolution:  0.1013212  #> * Time/frequency matrix summary #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's  #>  0.0000  0.0000  0.0000  0.0001  0.0001  0.0016    3044"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_piano_sample.html","id":null,"dir":"Reference","previous_headings":"","what":"A simple piano audio sample — ts_piano_sample","title":"A simple piano audio sample — ts_piano_sample","text":"sample frequency 11025 Hz.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_piano_sample.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"A simple piano audio sample — ts_piano_sample","text":"","code":"ts_piano_sample"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_piano_sample.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"A simple piano audio sample — ts_piano_sample","text":"numeric vector containing time series signal.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_440.html","id":null,"dir":"Reference","previous_headings":"","what":"Pure sine wave — ts_sin_440","title":"Pure sine wave — ts_sin_440","text":"Assuming sample rate 44100 Hz, sine wave's frequency 440 Hz.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_440.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Pure sine wave — ts_sin_440","text":"","code":"ts_sin_440"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_440.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Pure sine wave — ts_sin_440","text":"numeric vector containing time series signal.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_sin.html","id":null,"dir":"Reference","previous_headings":"","what":"A sinusoidal wave with varying frequency — ts_sin_sin","title":"A sinusoidal wave with varying frequency — ts_sin_sin","text":"frequency changing sinusoidal fashion.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_sin.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"A sinusoidal wave with varying frequency — ts_sin_sin","text":"","code":"ts_sin_sin"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_sin.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"A sinusoidal wave with varying frequency — ts_sin_sin","text":"numeric vector containing time series signal.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_superpos.html","id":null,"dir":"Reference","previous_headings":"","what":"Superimposed sine waves of different frequencies and different amplitudes — ts_sin_superpos","title":"Superimposed sine waves of different frequencies and different amplitudes — ts_sin_superpos","text":"Assuming sample rate 44100 Hz, superimposed signals' frequencies 440 Hz, 880 Hz, 100 Hz, 500 Hz, 1200 Hz 50 Hz.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_superpos.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Superimposed sine waves of different frequencies and different amplitudes — ts_sin_superpos","text":"","code":"ts_sin_superpos"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/ts_sin_superpos.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Superimposed sine waves of different frequencies and different amplitudes — ts_sin_superpos","text":"numeric vector containing time series signal.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/u.html","id":null,"dir":"Reference","previous_headings":"","what":"Augment physical unit — u","title":"Augment physical unit — u","text":"wrapper around units::set_units() mostly short name create dimensionful quantity.","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/u.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Augment physical unit — u","text":"","code":"u(x, unit = \"1\")"},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/u.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Augment physical unit — u","text":"x numeric vector augmented unit. unit character indicating unit. See units::valid_udunits() units::valid_udunits_prefixes() possible units.","code":""},{"path":[]},{"path":"https://lschneiderbauer.github.io/fCWTr/reference/u.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Augment physical unit — u","text":"","code":"u(10, \"km\") # 10 kilometer #> 10 [km] u(10, \"mm\") # 10 mm #> 10 [mm]  # comparison taking into account the unit u(100, \"m\") > u(1, \"km\") #> [1] FALSE"},{"path":"https://lschneiderbauer.github.io/fCWTr/news/index.html","id":"fcwtr-031","dir":"Changelog","previous_headings":"","what":"fCWTr 0.3.1","title":"fCWTr 0.3.1","text":"fix CRAN issues","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/news/index.html","id":"fcwtr-030","dir":"Changelog","previous_headings":"","what":"fCWTr 0.3.0","title":"fCWTr 0.3.0","text":"fcwt(): fix bug fcwt(..., n_freqs = 1, ...) leads faulty data representation. add freq_scale argument choose linear logarithmic frequency scale. allow (prefer) sample_freq, freq_begin, freq_end arguments passed dimensionful quantities, via u(). minor argument name changes. add new argument y_sample_freq allows specify sampling rate output signal. add meaningful default values arguments. fcwt_batch(): allow (prefer) sample_freq, freq_begin, freq_end time_resolution arguments passed dimensionful quantities, via u(). cases, averaging procedure together batching lead accidentally dropped duplicated time slices: mechanism overhauled, every slice perfectly aligned now, even averaged. shared argument fcwt(): changes fcwt(). new unit helper functions: u() du(): include improved physical unit treatment units package. Frequency time parameters can now “units” objects, created u(). Allow user adjust plot() scales use arbitrary time/frequency units. new helper functions determine correct value sigma given use case: sigma_res(), sigma_freq_res_rel(), sigma_from_time_res(), sigma_from_freq_res(), sigma_from_freq_res_rel(). add convenience S3 methods: print(), [], .matrix(), rbind(), tibble::as_tibble(). openmp_enabled()/avx_enabled() new functions check system OpenMP/AVX support. new vignette controlling time-frequency resolution vignette(\"sigma\"). add package logo","code":""},{"path":"https://lschneiderbauer.github.io/fCWTr/news/index.html","id":"fcwtr-021","dir":"Changelog","previous_headings":"","what":"fCWTr 0.2.1","title":"fCWTr 0.2.1","text":"CRAN release: 2024-06-17 Initial CRAN submission.","code":""}]