File:Circular convolution example.svg
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| DescriptionCircular convolution example.svg | English: Circular convolution can be expedited by the FFT algorithm, so it is often used with an FIR filter to efficiently compute linear convolutions. These graphs illustrate how that is possible. Note that a larger FFT size (N) would prevent the overlap that causes graph #6 to not quite match all of #3. | |||
| Date | ||||
| Source | Own work | |||
| Author | Bob K | |||
| Permission (Reusing this file) | I, the copyright holder of this work, hereby publish it under the following license:
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| Other versions | This file was derived from:Circular convolution example.png | |||
| SVG development InfoField |  This W3C-invalidvector image was created withLibreOffice. | |||
| Gnu Octave source InfoField | click to expand This graphic was created with the help of the following Octave script: % Optionsframe_background_gray=true;ifframe_background_graygraphics_toolkit("qt")% has "insert text" option% graphics_toolkit("fltk") % has cursor coordinate readoutframe_background=.94*[111];d=2;% amount to add to text sizeselsegraphics_toolkit("gnuplot")% background will be white regardless of value belowframe_background=.94*[111];d=0;endif%(https://octave.org/doc/v4.2.1/Graphics-Object-Properties.html#Graphics-Object-Properties)% Speed things up when using Gnuplotset(0,"DefaultFigureColor",frame_background)set(0,"DefaultAxesFontsize",10+d)% size of numeric tick labelsset(0,"DefaultTextFontsize",12+d)set(0,"DefaultAxesXtick",[])set(0,"DefaultAxesYtick",[])set(0,"DefaultLineLinewidth",1)xmax=3000;%=======================================================hfig=figure("position",[100100488512],"color",frame_background);x1=.02;% left marginx2=.02;% right marginy1=.08;% bottom margin for annotationy2=.08;% top margin for titledy=.04;% vertical space between rowswidth=1-x1-x2;height=(1-y1-y2-5*dy)/6;% space allocated for each of 6 rowsx_origin=x1;y_origin=1;% start at top of graph area%=======================================================y_origin=y_origin-y2-height;% position of top row% subplot() undoes all the "color" attempts above. (gnuplot bug)subplot("position",[x_originy_originwidthheight])L=100;f=ones(1,L)/L;plot(-100:200-1,[zeros(1,100)f*Lzeros(1,100)],"linewidth",2,"color","magenta")xlim([-100xmax]);ylim([02])title("Circular convolution example","fontsize",16)text(100,1.6,"h[n]")%text(xmax/2, 0.4, '\leftarrow n \rightarrow')text(2500,0.330,'\leftarrow n \rightarrow')y_origin=y_origin-dy-height;subplot("position",[x_originy_originwidthheight])a=[zeros(1,20)ones(1,L)zeros(1,300)0.5*ones(1,100)zeros(1,1000-L-20-400)];b=[zeros(1,1000-L-20)ones(1,L)zeros(1,20)];a1=[zeros(1,1000)azeros(1,1000)];b1=[zeros(1,1000)bzeros(1,1000)];plot(1:length(a1),a1,"color","blue",1:length(a1),b1,"color","red")xlim([0xmax]);ylim([02])text(200,1.6,"X[n]")y_origin=y_origin-dy-height;subplot("position",[x_originy_originwidthheight])a1=conv(a1,f);b1=conv(b1,f);plot(1:length(a1),a1+b1,"color","green","linewidth",2)xlim([0xmax]);ylim([02*max(a1)])text(200,1.6,"X[n] * h[n]")%text(200, 1.6, "X[n] ∗ h[n]", "interpreter","none") % requires PERL post-processory_origin=y_origin-dy-height;subplot("position",[x_originy_originwidthheight])a=[aaa];b=[bbb];L=1:length(a);plot(L,a,"color","blue",L,b,"color","red")xlim([0xmax]);ylim([02.5])set(gca,"xtick",[10002000]);%set(gca,"xticklabel",["N" "2N"])set(gca,"xticklabel",[]);text(981,-.5,"N");text(1955,-.5,"2N")text(200,2.0,'X_N[n]')y_origin=y_origin-dy-height;subplot("position",[x_originy_originwidthheight])a1=conv(a,f);b1=conv(b,f);b1(1:90)=b1(3000+[1:90]);L=1:length(a1);plot(L,a1,"color","blue",L,b1,"color","red")xlim([0xmax]);ylim([02*max(a1)])text(200,1.6,'components of X_N[n] * h[n]')% can't use "interpreter","none" herey_origin=y_origin-dy-height;subplot("position",[x_originy_originwidthheight])c=a1+b1;L=length(c);k=1100;plot(1:k,c(1:k),"color","red",k+(1:900),c(k+(1:900)),"color","green",..."linewidth",2,(k+900+1):xmax,c((k+900+1):xmax),"color","red")xlim([0xmax]);ylim([02*max(a1+b1)])text(200,1.6,'X_N[n] * h[n]')% can't use "interpreter","none" heretext(1263,-.6,"X[n] * h[n]","fontsize",16)%text(1274, -.6, "X[n] ∗ h[n]", "interpreter","none", "fontsize",16) % requires PERL post-processor% After a call to annotation(), the cursor coordinates change to the units used below.annotation("line",[.367.367],[.113.022])annotation("line",[.664.664],[.113.022]) |
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:17, 29 January 2020 | | 462 × 486(40 KB) | Bob K | replace white figure background with gray |
| 17:03, 9 June 2019 |  | 610 × 640(130 KB) | Bob K | fixed script typo (bug) | |
| 14:47, 7 June 2019 |  | 610 × 640(130 KB) | Bob K | reduce side margins | |
| 14:55, 5 June 2019 |  | 610 × 640(135 KB) | Bob K | enlarge xlabel of subplot 1 | |
| 13:50, 5 June 2019 |  | 512 × 537(332 KB) | Bob K | fix a problem with xlabel, caused by PERL post-processor (interferes with \leftarrow and \rightarrow) | |
| 13:29, 5 June 2019 |  | 512 × 537(332 KB) | Bob K | Replace a couple of asterisks with ∗ (∗). But this requires the Octave output file to be post-processed by the PERL script that is also used for window function plots. | |
| 14:01, 4 June 2019 |  | 610 × 640(135 KB) | Bob K | User created page with UploadWizard |
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| Width | 130.3mm |
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| Height | 137.16mm |
