Fundamental Frequency Estimation

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Loop Filter Identification

Dispersion Filter Design

Approximate Maximum Likelihood F0 Estimation

A periodic signal is a signal that forever repeats itself. — Click for http://en.wikibooks.org/wiki/Signals_and_Systems/Periodic_Signals

The Short Time Fourier Transform (STFT) computes the spectrum (DFT) of successive time frames of a signal. — Click for https://ccrma.stanford.edu/~jos/sasp/Short_Time_Fourier_Transform.html

Pitch is the perceived fundamental frequency of a sound. — Click for http://en.wikipedia.org/wiki/Pitch_(music)

Noise (in signal processing) is a random signal. In the language of statistical signal processing, a noise signal is typically modeled as 'stochastic process', which is in turn defined as a sequence of random variables. — Click for https://ccrma.stanford.edu/~jos/sasp/What_Noise.html

A signal is typically a real-valued function of time. A discrete-time signal is typically a real-valued function of discrete time, and is therefore a time-ordered sequence of real numbers. — Click for http://ccrma.stanford.edu/~jos/filters/Definition_Signal.html

Click for https://ccrma.stanford.edu/~jos/pasp/Ideal_Plucked_String.html

Fast Fourier Transforms (FFT) are fast algorithms for computing the Discrete Fourier Transform (DFT) — Click for https://ccrma.stanford.edu/~jos/mdft/Fast_Fourier_Transform_FFT.html

Click for https://ccrma.stanford.edu/~jos/pasp/Length_FIR_Loop_Filter.html

Click for https://ccrma.stanford.edu/~jos/mdft/Exponentials.html

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If the mass of a harmonic oscillator is excited, the system responds by vibrating back and forth. Whenever the mass is at its rest position, the system contains only kinetic energy. Conversely, whenever the mass velocity is zero, the system contains only potential energy. — Click for http://ccrma.stanford.edu/realsimple/lab_inst/Background.html

Every periodic signal has a fundamental frequency given by the inverse of the period. If the period is in units of seconds, then the fundamental frequency is in units of Hertz (cycles per second). According to Fourier theory, every periodic signal can be expressed as a sum of sinusoids at frequencies given by integer multiples of the fundamental frequency. For integers greater than 1, these frequencies are called harmonic frequencies, and the sinusoids at harmonic frequencies are typically called harmonics. — Click for https://www.physicsclassroom.com/class/sound/Lesson-4/Fundamental-Frequency-and-Harmonics

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Index of terms in JOS Website

Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Loop Filter Identification

Dispersion Filter Design

Approximate Maximum Likelihood F0 Estimation

Fundamental Frequency Estimation

As mentioned in §6.11.2 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 [474]:

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 $\Delta f_i$
The pitch estimate ${\hat f}_0$ is defined as the most common spacing $\Delta f_i$ 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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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Fundamental Frequency Estimation

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University