Minimum Zero-Padding for High-Frequency Peaks

Table 4.3 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 4.3 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.^5.13

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.