## Fast Transforms in Audio DSP

Since most audio signal processing applications benefit from
*zero padding* (see §8.1), in which case we can always
choose the FFT length to be a power of 2, there is almost never a need
in practice for more ``exotic'' FFT algorithms than the basic
``pruned'' power-of-2 algorithms. (Here ``pruned'' means elimination
of all unnecessary operations, such as when the input signal is real
[74,21].)

An exception is when processing exactly periodic signals where the
period is known to be an exact integer number of samples in
length.^{A.8} In such a case, the DFT of one period of the waveform can be
interpreted as a *Fourier series* (§B.3)
of the periodic waveform, and
unlike virtually all other practical spectrum analysis scenarios,
spectral interpolation is not needed (or wanted). In the exactly
periodic case, the spectrum is truly zero between adjacent harmonic
frequencies, and the DFT of one period provides spectral samples only
at the harmonic frequencies.

Adaptive FFT software (see §A.7 below) will choose the fastest algorithm available for any desired DFT length. Due to modern processor architectures, execution time is not normally minimized by minimizing arithmetic complexity [23].

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Related Transforms

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Bluestein's FFT Algorithm