fix typo

vignettes/sigma.Rmd

@@ -18,7 +18,7 @@ The continuous wavelet transform (CWT) essentially evaluates a correlation funct
 
 In contrast to the [Short Time Fourier Transform](https://en.wikipedia.org/wiki/Short-time_Fourier_transform), where the window size does not depend on the frequency, the CWT models a frequency-dependent window size by the frequency depending spread of the Gaussian envelope.[^1]
 
-[^1]: That is of course one of the selling points of the CWT: it works for all frequency ranges, while the fixed window size in the Short Time Fourier Transform will break down when probing modes whose wavelength approach the window size, at the same time it lacks a reasonable time resolutions for modes whose wavelenght is much smaller than the window size.
+[^1]: That is of course one of the selling points of the CWT: it works for all frequency ranges, while the fixed window size in the Short Time Fourier Transform will break down when probing modes whose wavelength approach the window size, at the same time it lacks a reasonable time resolutions for modes whose wavelength is much smaller than the window size.
 
 For a particular time $t$ and a reference frequency $f$, the Gaussian envelope $g(t, f)$ of the wavelet is given by $$g(t, f) \sim e^{-\left( \frac{t f}{2 \sigma} \right)^2}$$ with variance in time $\Delta t=\frac{\sigma}{f}$ which also sets the scale for the effective time resolution of the CWT at frequency $f$. The corresponding frequency resolution is given by the spreading of the Gaussian envelope in Fourier space: $\Delta f = \frac{f}{2\pi \sigma}$. The time and frequency resolution satisfy the famous time-frequency uncertainty relation $\Delta t \Delta f=\frac{1}{2\pi}$.