Table 5.3 gives zero-padding factors sufficient for keeping the bias below Hz, where denotes the sampling rate in Hz, and is the window length in samples. For fundamental frequency estimation, can be interpreted as the relative frequency error `` '' when the window length is one period. In this case, is the fundamental frequency in Hz. More generally, is the bandwidth of each side-lobe in the DTFT of a length rectangular, generalized Hamming, or Blackman window (any member of the Blackman-Harris window family, as elaborated in Chapter 3).
Note from Table 5.3 that the Blackman window requires no zero-padding at all when only % accuracy is required in peak-frequency measurement. It should also be understood that a frequency error of % is inaudible in most audio applications.6.10
Minimum Zero-Padding for Low-Frequency Peaks
Matlab for Parabolic Peak Interpolation