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To summarize, zero-padding is used for

  • padding out to the next higher power of 2 so a Cooley-Tukey FFT can be used with any window length,
  • improving the quality of spectral displays, and
  • oversampling spectral peaks so that some simple final interpolation will be accurate.
In addition, we will learn in Chapter 8 that zero-padding is also necessary to accommodate spectral modifications in the short-time Fourier transform (STFT). This is because spectral modifications cause the time-domain signal to lengthen in time, and without sufficient zero-padding to accommodate it, there will be time aliasing in the reconstruction of the signal from the modified FFTs.

Some examples of interpolated spectral display by means of zero-padding may be seen in §3.4.

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Index Ranges for Zero-Phase Zero-Padding