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 @ 0.03 tt D Sin @ 0.1 tt D + 0.5 Random @ Real, - 1, 1 D , 8 tt, 1, 1024, 1 <D ; dataplot = ListPlot @ fakedata, PlotJoined ® True, PlotLabel -> "sample data" D ; fullfft = Fourier @ fakedata D ; ListPlot @ Abs @ fullfft D , PlotJoined ® True, PlotRange -> All , PlotLabel ® "Fourier transform" D ; filterfn = Table @ Exp @ - jj^2 ± 8000 D + Exp @ - H jj - 1024 L ^2 ± 8000 D , 8 jj, 1, 1024 <D ; ListPlot @ Abs @ filterfn D , PlotJoined ® True, PlotRange -> All , PlotLabel ® "Filter function" D ; filterfft = filterfn fullft; ListPlot @ Abs @ filterfft D , PlotJoined ® True, PlotRange -> All , PlotLabel -> " Filtered Fourier transform" D ; filterback =
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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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This note was uploaded on 12/29/2011 for the course PHYSICS 375 taught by Professor Eno during the Spring '11 term at Maryland.

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

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