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The Fourier Transform: What's Wrong with It?

FFTs do exactly what they are designed to: transform a function of time into a function of frequency; however, challenges arise in practical applications..

“Standard” options include Nth octave, shock response spectra (SRS), and enhancements to the Fourier Transform such as Power Spectral Density (PSD). In 1965, James Cooley and John Tukey recognized that, for arrays that were a power of 2 in length, many of the operations were duplicated and they developed an algorithm, the “Fast Fourier Transform”, that significantly reduced the number of calculations required. I have demonstrated some of the vagaries of the Fourier Transform and shown that it is perfect in concept but must be manipulated in most real cases because we don’t have an infinitely long time history.

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