diff --git a/debugging/lecture/debugging-chapter.pdf b/debugging/lecture/debugging-chapter.pdf index d4df870..5faa385 100644 Binary files a/debugging/lecture/debugging-chapter.pdf and b/debugging/lecture/debugging-chapter.pdf differ diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index 1dfe6f5..c1478a9 100644 --- a/pointprocesses/lecture/pointprocessscetchA.eps +++ b/pointprocesses/lecture/pointprocessscetchA.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchA.tex %%Creator: gnuplot 4.6 patchlevel 4 -%%CreationDate: Sat Nov 19 10:17:42 2016 +%%CreationDate: Tue Nov 14 09:22:04 2017 %%DocumentFonts: %%BoundingBox: 50 50 373 135 %%EndComments @@ -430,10 +430,10 @@ SDict begin [ /Title (pointprocessscetchA.tex) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 4) - /Author (jan) + /Author (benda) % /Producer (gnuplot) % /Keywords () - /CreationDate (Sat Nov 19 10:17:42 2016) + /CreationDate (Tue Nov 14 09:22:04 2017) /DOCINFO pdfmark end } ifelse diff --git a/pointprocesses/lecture/pointprocessscetchA.pdf b/pointprocesses/lecture/pointprocessscetchA.pdf index b532798..2dcdf91 100644 Binary files a/pointprocesses/lecture/pointprocessscetchA.pdf and b/pointprocesses/lecture/pointprocessscetchA.pdf differ diff --git a/pointprocesses/lecture/pointprocessscetchB.eps b/pointprocesses/lecture/pointprocessscetchB.eps index 1856ba8..f2ccaf3 100644 --- a/pointprocesses/lecture/pointprocessscetchB.eps +++ b/pointprocesses/lecture/pointprocessscetchB.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchB.tex %%Creator: gnuplot 4.6 patchlevel 4 -%%CreationDate: Sat Nov 19 10:17:43 2016 +%%CreationDate: Tue Nov 14 09:22:05 2017 %%DocumentFonts: %%BoundingBox: 50 50 373 237 %%EndComments @@ -430,10 +430,10 @@ SDict begin [ /Title (pointprocessscetchB.tex) /Subject (gnuplot plot) /Creator (gnuplot 4.6 patchlevel 4) - /Author (jan) + /Author (benda) % /Producer (gnuplot) % /Keywords () - /CreationDate (Sat Nov 19 10:17:43 2016) + /CreationDate (Tue Nov 14 09:22:05 2017) /DOCINFO pdfmark end } ifelse diff --git a/pointprocesses/lecture/pointprocessscetchB.pdf b/pointprocesses/lecture/pointprocessscetchB.pdf index 6e4e783..7fce211 100644 Binary files a/pointprocesses/lecture/pointprocessscetchB.pdf and b/pointprocesses/lecture/pointprocessscetchB.pdf differ diff --git a/spectral/lecture/spectral.tex b/spectral/lecture/spectral.tex index 28d37d2..517e7aa 100644 --- a/spectral/lecture/spectral.tex +++ b/spectral/lecture/spectral.tex @@ -2,18 +2,35 @@ 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}