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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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pointprocesses/lecture/pointprocessscetchB.eps
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%%Title: pointprocessscetchB.tex %%Title: pointprocessscetchB.tex
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@ -430,10 +430,10 @@ SDict begin [
/Title (pointprocessscetchB.tex) /Title (pointprocessscetchB.tex)
/Subject (gnuplot plot) /Subject (gnuplot plot)
/Creator (gnuplot 4.6 patchlevel 4) /Creator (gnuplot 4.6 patchlevel 4)
/Author (jan) /Author (benda)
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spectral/lecture/spectral.tex
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This is a stub that should be filled :) This is a stub that should be filled :)
\section{The Fourier space} % \section{The Fourier space}
\section{The Fourier Transform} \section{The Fourier Transform}
Complex numbers... magnitude and phase
\subsection{Fast Fourier transform} \subsection{Fast Fourier transform}
\section{Power spectrum} \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{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} \section{Coherence function}
\subsection{Forward and reverse filter}