Matlab for Computing Minimum Zero-Padding Factors

The minimum zero-padding factors in the previous two subsections were computed using the matlab function zpfmin listed in §G.2.4. For example, both tables above are included in the output of the following matlab program:

  windows={'rect','hann','hamming','blackman'};
  freqs=[1000,500,250,125,62.5];
  for i=1:length(windows)
    w = sprintf("%s",windows(i))
    for j=1:length(freqs)
      f = freqs(j);
      zpfmin(w,1/f,0.01*f)  % 1 percent spec (large for audio)
      zpfmin(w,1/f,0.001*f) % 0.1 percent spec (good > 1 kHz)
      zpfmin(w,1/f,1)       % 1 Hz spec (good below 1 kHz)
    end
  end

In addition to ``perceptually exact'' detection of spectral peaks, there are times when we need to find spectral parameters as accurately as possible, irrespective of perception. For example, one can estimate the stiffness of a piano string by measuring the stretched overtone-frequencies in the spectrum of that string's vibration. Additionally, we may have measurement noise, in which case we want our measurements to be minimally influenced by this noise. The following sections discuss optimal estimation of spectral-peak parameters due to sinusoids in the presence of noise.

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Next: Least Squares Sinusoidal Parameter Estimation

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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.