Last night a friend from Vanderbilt, Father John Rickert, sent me a curious math problem. (John was a PhD student…
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Gibbs phenomenon
I realized recently that I’ve written about generalized Gibbs phenomenon, but I haven’t written about its original context of Fourier…
Continue ReadingSquare wave, triangle wave, and rate of convergence
There are only a few examples of Fourier series that are relatively easy to compute by hand, and so these…
Continue ReadingClipped sine waves
One source of distortion in electronic music is clipping. The highest and lowest portions of a wave form are truncated…
Continue ReadingSine series for a sine
The Fourier series of an odd function only has sine terms—all the cosine coefficients are zero—and so the Fourier series…
Continue ReadingFourier Transformation and Its Mathematics
Here is an example of how the form of the signal changes with the change in sampling rate :Let the original…
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