Pitch Detection from Sinusoidal Peaks

Given a set of sinusoidal peak frequencies , , it is straightforward to form a pitch estimate. Here we assume that ``pitch'' means the same thing as ``fundamental frequency'' or ``F0'', i.e., that the signal is periodic, so that all of its sinusoidal components are harmonics of the fundamental frequency F0. For inharmonic sounds, the perceived pitch can be complex to predict.

The F0-detection algorithm described in this section consists of the following steps:

1. Find the peak of the histogram of the peak-frequency-differences in order to find the most common harmonic spacing. This is the nominal pitch estimate.
2. Refine the nominal pitch estimate using linear regression. Linear regression simply fits a straight line through the date to give a least-squares fit.

The slope of the fitted line gives the pitch estimate.

In many cases, results are improved through the use of preprocessing of the spectrum prior two peak finding. Examples include the following:

• Pre-emphasis: Equalize the spectrum so as to flatten it

• Masking: Small peaks close to much larger peaks are often masked by the auditory system. Therefore, it is good practice to reject all peaks below an inaudibility threshold which is the maximum of the threshold of hearing (versus frequency) and the masking pattern generated by the largest peaks. Since it is simple to extract peaks in descending magnitude order, each removed peak can be replaced by its masking pattern, which elevates the assumed inaudibility threshold.

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Subsections

• • References on F0 Estimation

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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.