Fundamental Frequency Estimation

As mentioned in §4.11.2 above, it is advisable to estimate the fundamental frequency of vibration (often called ``F0'') in order that the partial overtones are well resolved while maintaining maximum time resolution for estimating the decay time-constant.

Below is a summary of the F0 estimation method used in calibrating loop filters with good results [483]:

• Take an FFT of the middle third of a recorded plucked string tone.
• Find the frequencies and amplitudes of the largest peaks, where is chosen so that the retained peaks all have a reasonable signal-to-noise ratio.
• Form a histogram of peak spacing
• The pitch estimate is defined as the most common spacing in the histogram.

The F0 estimate so formed is sufficiently accurate for purposes of calibrating a peak tracker for decay-rate estimation. (The F0 value is only used to set the FFT window length in the STFT to four nominal periods under the window, so it is not critical.)

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Subsections

• Approximate Maximum Likelihood F0 Estimation
• References on F0 Estimation
• Extension to Stiff Strings

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written by 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.