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added a few things to spectral

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Jan Benda 2017-11-24 15:09:04 +01:00
parent cfd5477fa1
commit 35d1b908f3
6 changed files with 26 additions and 9 deletions
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debugging/lecture/debugging-chapter.pdf
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pointprocesses/lecture/pointprocessscetchA.eps
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%%CreationDate: Tue Nov 14 09:22:04 2017
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pointprocesses/lecture/pointprocessscetchB.eps
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%!PS-Adobe-2.0 EPSF-2.0
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%%CreationDate: Tue Nov 14 09:22:05 2017
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@ -430,10 +430,10 @@ SDict begin [
/Title (pointprocessscetchB.tex)
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/CreationDate (Tue Nov 14 09:22:05 2017)
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spectral/lecture/spectral.tex
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This is a stub that should be filled :)
\section{The Fourier space}
% \section{The Fourier space}
\section{The Fourier Transform}
Complex numbers... magnitude and phase
\subsection{Fast Fourier transform}
\section{Power spectrum}
\[ S_{x,x} = |X(f)|^2 \]
Parceval theorem:
\[ \int_{-\infty}^{+\infty} x(t)^2 dt = \int_{-\infty}^{+\infty} |X(f)|^2 df \]
Autocorrelation:
Wiener-Kinchin theorem:
\[ {\cal F}\{Corr(x,x)\} = |X(f)|^2 \]
\section{Spectrogram}
\section{Transfer function}
\section{Cross spectrum}
\[ S_{x,y} = X(f)Y^*(f) \]
is complex valued (magnitude and phase)!
\section{Forward and reverse filter}
Correlation theorem:
\[ {\cal F}\{Corr(x,y)\} = X(f)Y^*(f) = S_{x,y} \]
\section{Transfer function}
\section{Coherence function}
\subsection{Forward and reverse filter}