Matlab for the Periodogram

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Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

The Periodogram

Welch's Method

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

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

White noise is a random signal in which all frequencies are equally present over time. It is analogous to white light which, as Isaac Newton first realized, consists of the superposition of all visible light frequencies. — Click for https://ccrma.stanford.edu/~jos/sasp/White_Noise.html

Matlab is a high-level scripting language for scientific computing — Click for https://ccrma.stanford.edu/~jos/matlab/

A periodogram may be defined as the squared-magnitude of a Discrete Fourier Transform (DFT) divided by the DFT length. — Click for https://ccrma.stanford.edu/~jos/sasp/Periodogram.html

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Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

The Periodogram

Welch's Method

Matlab for the Periodogram

Octave and the Matlab Signal Processing Toolbox have a periodogram function. Matlab for computing a periodogram of white noise is given below (see top-right plot in Fig.6.1):

M = 32;
v = randn(M,1);       % white noise
V = abs(fft(v)).^2/M; % periodogram

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Matlab for the Periodogram

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1. Copyright © 2022-02-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University