Last night a friend from Vanderbilt, Father John Rickert, sent me a curious math problem. (John was a PhD student…

Continue Reading# fourier

## 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 Reading## Square 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 Reading## Clipped sine waves

One source of distortion in electronic music is clipping. The highest and lowest portions of a wave form are truncated…

Continue Reading## Sine 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 Reading## Fourier 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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