Moving Average

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

Answer 1

[Image Analyst]

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);
plot(y);
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);
plot(kernel);
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);
plot(filtered_y);
grid on;
ylim([0 1]);
title('filtered y (the filtered data)', 'FontSize', fontSize);

[Daniel Shub]

Nice demo, care to comment on why you chose conv over filter?

[Image Analyst]

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.

Answer 2

[Daniel Shub]

Typically people use

doc conv

to do moving averages

[Jan]

Or FILTER. Usually the parameters of a moving average filter do *not* reach 1 at the center.

[Daniel Shub]

Is there an advantage of filter over conv (or conv over filter) in this case? I think I usually use conv with fir filters and filter with iir filters, but I haven't really thought about it in a long time.

[Titus Edelhofer]

Yes: the documentation of filter contains an example of how to use filter for a moving average ;-).

[Jan]

@Daniel: I'm not happy with the implementation of FILTER. E.g. the multi-threading starts only, if the signal has more than 16 columns. Therefore I've re-implemented this function as C-Mex, which is surprisingly faster.

I have not seen speed problems with CONV yet - are the C-sources still included in Matlab 2012a?

[Daniel Shub]

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]

FILTER handles complex signals and complex filter parameters. As far as I remember, conv2.c accepts real DOUBLEs only - perhaps SINGLEs in addition.