A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

Introduction of C Programming for DSP Applications

Applications of the STFT

Fundamental Frequency Estimation from Sinusoidal Peaks

**Search Spectral Audio Signal Processing**

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Sinusoidal peak measurement was discussed in Chapter 4.
Given a set of sinusoidal peak frequencies ,
, it
is usually straightforward to form a *fundamental frequency*
estimate ``''. This task is also called *pitch detection*,
where the perceived ``pitch'' of the audio signal is assumed to
coincide well enough with its fundamental frequency. We assume here that
the signal is *periodic*, so that all of its sinusoidal
components are *harmonics* of the fundamental frequency .
(For inharmonic sounds, the perceived pitch, if any, can be complex to
predict [54].)

An approximate maximum-likelihood -detection
algorithm^{10.1} consists
of the following steps:

- 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. - Refine the nominal pitch estimate using
*linear regression*. Linear regression simply fits a straight line through the data to give a least-squares fit. - The slope of the fitted line gives the pitch estimate.

A matlab listing for F0 estimation along these lines appears in §G.6.

Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and (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.

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