File:Correlation function.svg
![File:Correlation function.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/8/86/Correlation_function.svg/600px-Correlation_function.svg.png)
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Summary
DescriptionCorrelation function.svg | English: The blue curve is the cross-correlation of a square wave and a cosine function, as the phase lag of the cosine varies over one cycle. The amplitude and phase lag at the maximum value are the polar coordinates of one harmonic in the Fourier series expansion of the square wave. The corresponding Cartesian coordinates can be determined by evaluating the cross-correlation at just two phase lags separated by 90º. | |||
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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SVG development InfoField | ![]() This W3C-invalid vector image was created with LibreOffice. | |||
Gnu Octave source InfoField | click to expand This graphic was created with the help of the following Octave script: graphics_toolkit gnuplot pkg load signal #{ The gnuplot graphics toolkit is not actively maintained and has a number of limitations that are unlikely to be fixed. Communication with gnuplot uses a one-directional pipe and limited information is passed back to the Octave interpreter so most changes made interactively in the plot window will not be reflected in the graphics properties managed by Octave. For example, if the plot window is closed with a mouse click, Octave will not be notified and will not update its internal list of open figure windows. The qt toolkit is recommended instead. #} set(0, "DefaultAxesTitleFontWeight", "bold") set(0, "DefaultAxesFontWeight", "bold") set(0, "DefaultAxesFontSize", 14) P = 2000; % signal duration x = 0:P-1; % sampling times % Any function will do for the signal. It needn't be periodic, but a square wave is convenient. period=233; % square wave period s = square((x-period*.67)*2*pi/period); n = 4; % a harmonic (any harmonic will do) num_angles=1000; % eval the correlation function at 1000 phases correl = []; phi = (0:1:num_angles-1)/num_angles; for m=phi % The right-hand side is equivalent to sum(s.*cos(2*pi*(n/P*x - m)) correl(end+1) = real(sum(s.*exp(-i*2*pi*(n/P*x - m)))); endfor figure("position",[1 1 700 700]) plot(phi*360, correl, "color","b", "linewidth",3) xlim([0 360]); set(gca, 'xtick', [0 1 2 3 4]*90); [maxval,idx] = max(correl); cossin = sum(s.*exp(i*2*pi*n*x/P)) % The next two things are equal mod(atan2(imag(cossin), real(cossin))*360/(2*pi), 360) (idx-1)*360/num_angles % The next two things are equal maxval abs(cossin) hold on stem((idx-1)*360/num_angles, correl(idx), "filled", "linewidth",4, "color",[1 0 1], "markerfacecolor",[1 0 1]) stem( 0,correl( 0*num_angles/360+1),"filled", "linewidth",4, "color",[1 0 1], "markerfacecolor", [1 0 1]) stem(90,correl(90*num_angles/360+1),"filled", "linewidth",4, "color",[1 0 1], "markerfacecolor", [1 0 1]) title("Cross-correlation function", "fontsize",14); xlabel("phase lag (degrees)", "fontsize",14) ylabel("correlation amplitude", "fontsize",14) |
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Captions
Example of using two points of a correlation function to determine the location and height of its maximum
Items portrayed in this file
depicts
11 April 2022
image/svg+xml
09d1bd458779569d05dacbd6a5732edae1476426
70,305 byte
765 pixel
765 pixel
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 03:19, 12 April 2022 | ![]() | 765 × 765 (69 KB) | Bob K | Uploaded own work with UploadWizard |
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Width | 215.9mm |
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Height | 215.9mm |
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