37 lines
731 B
TeX
37 lines
731 B
TeX
\chapter{Spectral analyses}
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This is a stub that should be filled :)
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% \section{The Fourier space}
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\section{The Fourier Transform}
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Complex numbers... magnitude and phase
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\subsection{Fast Fourier transform}
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\section{Power spectrum}
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\[ S_{x,x} = |X(f)|^2 \]
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Parceval theorem:
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\[ \int_{-\infty}^{+\infty} x(t)^2 dt = \int_{-\infty}^{+\infty} |X(f)|^2 df \]
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Autocorrelation:
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Wiener-Kinchin theorem:
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\[ {\cal F}\{Corr(x,x)\} = |X(f)|^2 \]
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\section{Spectrogram}
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\section{Cross spectrum}
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\[ S_{x,y} = X(f)Y^*(f) \]
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is complex valued (magnitude and phase)!
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Correlation theorem:
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\[ {\cal F}\{Corr(x,y)\} = X(f)Y^*(f) = S_{x,y} \]
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\section{Transfer function}
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\section{Coherence function}
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\subsection{Forward and reverse filter}
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