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Moving Average

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khatereh on 28 Mar 2012
I have a plot of residuals vs Distance and I want to run moving average window over it to capture the trend. My window should have a cos fun on both side and then reach the value of 1 between these two. I don't know how should I code it up?Thankss

Answers (2)

Image Analyst
Image Analyst on 28 Mar 2012
Perhaps this demo will be instructive for you:
clc; % Clear the command window.
workspace; % Make sure the workspace panel is showing.
fontSize = 20;
% Make sample data
y = rand(1,100)
subplot(2, 2, 1);
grid on;
ylim([0 1]);
windowWidth = 15;
t = 1:windowWidth;
title('Y (the data)', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Give a name to the title bar.
set(gcf,'name','Demo by ImageAnalyst','numbertitle','off')
% Construct cosine kernel
kernel = cos(2*pi*(t - ceil(windowWidth/2))/ (2*windowWidth));
subplot(2, 2, 2);
grid on;
ylim([0 1]);
title('The cosine kernel', 'FontSize', fontSize);
% Normalize kernel so that mean of filtered data
% will be the same as the mean of the original data.
kernel = kernel / sum(kernel);
% Now filter the data with the normalized cosine kernel.
filtered_y = conv(y, kernel);
subplot(2, 2, 3);
grid on;
ylim([0 1]);
title('filtered y (the filtered data)', 'FontSize', fontSize);
Daniel Shub
Daniel Shub on 28 Mar 2012
Nice demo, care to comment on why you chose conv over filter?
Image Analyst
Image Analyst on 28 Mar 2012
No reason really. I'm just more familiar with conv() because of my optics background. I also use conv2 from habit even though there is imfilter that does the same thing without the flipping that convolution does. 'Course it doesn't matter for symmetrical kernels. I probably should use imfilter instead of conv2 because I think Jeff said he optimized that a great deal so that it's actually faster than conv2.

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Daniel Shub
Daniel Shub on 28 Mar 2012
Typically people use
doc conv
to do moving averages
Daniel Shub
Daniel Shub on 28 Mar 2012
I couldn't find the c source for conv/conv2 r2011a. When there are a number of "identical" functions for solving a problem, I find my intuition is close to worthless. This isn't so bad since I don't spend much time optimizing or dealing with things that push numerical stability.
Jan on 28 Mar 2012
FILTER handles complex signals and complex filter parameters. As far as I remember, conv2.c accepts real DOUBLEs only - perhaps SINGLEs in addition.

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