Integral average of y values with respect to x values
11 views (last 30 days)
Show older comments
I have two vectors (x and y) of the same size with x having more than one value in the y direction. For example, x is [0.02 0.02 0.03 0.03 0.03 0.04 0.04 0.05 0.05 0.05] and y is [0.23 0.40 0.12 0.16 0.09 0.50 0.02 0.33 0.10 0.08]. I want to convert the attached scattered plot of the two vectors to a simple continuous curve, by evaluating the integral average of y values with respect to x values. Take into account that the x vector is already ordered from small to large values. How could I do this? Thank you in advance.
1 Comment
Image Analyst
on 5 Oct 2015
"I have two vectors (x and y) of the same size with x having more than one value in the y direction" Huh? Does it have one more, or are x and y the same length? Not sure what you're saying. Are you saying that for any given x value, it may be in the x array more than once, with each occurrence of that x value having a different y value stored at corresponding indexes in the y array?
Accepted Answer
Star Strider
on 4 Oct 2015
I’m not exactly certain what you want, but one approach would be to use the cumtrapz function:
x = [0.02 0.02 0.03 0.03 0.03 0.04 0.04 0.05 0.05 0.05];
y = [0.23 0.40 0.12 0.16 0.09 0.50 0.02 0.33 0.10 0.08];
I = cumtrapz(x,y); % Integrated Vector Of ‘y’ w.r.t. ‘x’
figure(1)
plot(x, I)
grid
7 Comments
Star Strider
on 5 Oct 2015
I would experiment with the filter order and use filtfilt if you have the Signal Processing Toolbox. This gave what appeared to me to be close to what you want:
N = 50; % Length Of Filter
b = ones(1,N); % Filter Coefficients
a = N; % Filter Coefficients
sf = filtfilt(b, a, Vsorted); % Filter Data
I experimented with filter lengths ranging from 50 to 200 and it seemed to give the result you illustrated. It is not possible to design a typical low-pass filter because your data are not regularly sampled. It would be necessary to interpolate your data (using interp1 if your data meet its requriements) to a regularly-sampled time base (here Rsorted) to design a filter for it. That could make the curve smoother, but I can’t promise that it would be.
The first step after interpolation would be to do a fft in order to determine what frequencies you want to exclude as noise. When you decide on a cutoff frequency for your low-pass filter, I would then use the filter design procedure I outlined here.
More Answers (1)
arich82
on 5 Oct 2015
Edited: arich82
on 5 Oct 2015
[edited to fix typo in comments, and clean-up useless clutter]
Perhaps try combining the filter solution with the accumarray (or filtfilt, if you have the appropriate toolbox, which I do not):
x = Rsorted(:).';
y = Vsorted(:).';
% compute average y for each unique x
[c, ic, ia] = unique(x);
sums = accumarray(ia, y);
wgts = accumarray(ia, ones(size(y))); % weights, i.e. number of reps
avgs = sums./wgts;
% interpolate data on regular grid
n = numel(c); % or some other number
xq = linspace(c(1), c(end), n);
yq = interp1(c, avgs, xq);
% filter gridded data
windowSize = 50;
a = windowSize;
b = ones(1, windowSize);
yf = filter(b, a, yq);
% plot results
hold all;
plot(xq, yf, 'r-', 'LineWidth', 3)
4 Comments
See Also
Categories
Find more on Digital Filtering in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!