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Filtering with FFTs

# Filtering with FFTs - Fourier filterfft D fdplot = ListPlot...

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Filtering with Fourier Transforms A demonstration of how to remove high frequency noise from data by Fourier transforming, filtering, and Fourier transforming back. fakedata Table Sin 0.03tt Sin 0.1tt 0.5Random Real, 1, 1 , tt, 1, 1024, 1 ; dataplot ListPlot fakedata, PlotJoined True, PlotLabel "sample data" ; fullfft Fourier fakedata ; ListPlot Abs fullfft , PlotJoined True, PlotRange All, PlotLabel "Fourier transform" ; filterfn Table Exp jj^2 8000 Exp jj 1024 ^2 8000 , jj, 1, 1024 ; ListPlot Abs filterfn , PlotJoined True, PlotRange All, PlotLabel "Filter function" ; filterfft filterfnfullft; ListPlot Abs filterfft , PlotJoined True, PlotRange All, PlotLabel

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Unformatted text preview: Fourier @ filterfft D ; fdplot = ListPlot @ Reverse @ Re @ filterback D , PlotJoined ® True, PlotRange ® All, PlotStyle ® RGBColor @ 1, 0, 0 D , PlotLabel ® " FFT of filtered FFT" D ; Show @ dataplot, fdplot D 200 400 600 800 1000-1.5-1-0.5 0.5 1 sample data 200 400 600 800 1000 2 4 6 8 Fourier transform 200 400 600 800 1000 0.2 0.4 0.6 0.8 1 Filter function 2 Filtering with FFTs.nb 200 400 600 800 1000 2 4 6 Filtered Fourier transform 200 400 600 800 1000-1-0.5 0.5 FFT of filtered FFT Filtering with FFTs.nb 3 200 400 600 800 1000-1.5-1-0.5 0.5 1 sample data ± Graphics ± 4 Filtering with FFTs.nb...
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