Find peaks/valleys of a noisy signal

I have this signal which is noisy as well as it has too much data samples. When I try to find the peaks or valleys, it gives multiple peaks/valleys around the same point probably because the data is noisy and has too many samples. I did use the 'MinPeakDistance' and also tried using the 'MinPeakHeight' and also the 'Threshold' but all time I get many peaks's around a given time instant. In other words, I would want only one peak at the peak of the signal and one valley at the trough of the signal. I have the data attached to the post too. Thanks in advance.

It is just a two column data and I plot the 2nd column wrt 1st one. I would prefer to measure valleys and I would actually need both.

[pks locs] = findpeaks(data_compact(:,2),'MinPeakHeight',0.992*max(data_compact(:,2)),'MinPeakDistance',5000e-3); % peaks
data_inverted(:,1) = data_compact(:,1);
data_inverted(:,2) = -data_compact(:,2);
%[valley valleys_locs] = findpeaks(data_inverted(:,2),'MinPeakDistance',0.2e-3); % valleys

[Paul Hoffrichter]

I think the .mat file does not match the figure.

[Image Analyst]

I think he just included a small subset of the data.

s = load('data_compact.mat')
data_compact = s.data_modified;
% Smooth with a savitzky-golay filter
% data_compact(:, 2) = sgolayfilt(data_compact(:, 2), 2, 151);
plot(data_compact(:,1), data_compact(:,2), 'b-');
grid on;

[pks, locs] = findpeaks(data_compact(:,2),'MinPeakHeight',0.992*max(data_compact(:,2)),'MinPeakDistance',5000e-3); % peaks
hold on;
plot(data_compact(locs, 1), pks, 'r.', 'MarkerSize', 10);

% Find Valleys
data_inverted(:,1) = data_compact(:,1);
data_inverted(:,2) = -data_compact(:,2);

% [valleyValues valleysIndexes] = findpeaks(data_inverted(:,2),'MinPeakDistance',0.2e-3); % valleys
% plot(data_inverted(valleysIndexes, 1), -valleyValues, 'r.', 'MarkerSize', 10);

[Jay Vaidya]

Yes, so this has many peaks (red) on a single peak of the signal as you can see in the image. This might be because of the noise, but I would like only one peak and hence, I want to count the total number of peaks in this signal which is my end goal.

[Jay Vaidya]

Hello Image Analyst, could you please remove the data if possible?

[Walter Roberson]

The data is part of the question; the question does not make sense without the data.

[Jay Vaidya]

Yes, but I would like to put another data instead of this data, as this is not that important to what I am intending to do. I also cannot delete the question. I currently don't need to solve this problem and the data can be misused.

[Walter Roberson]

No-one knows what your data means, or who or what it was created from. It is therefore difficult to "misuse".

https://en.wikipedia.org/wiki/Streisand_effect

Answer 1

[Image Analyst]

Try this:

clc;    % Clear the command window.
clear all;
close all;
workspace;  % Make sure the workspace panel is showing.
format short g;
format compact;
fontSize = 22;
fprintf('Beginning to run %s.m ...\n', mfilename);

%--------------------------------------------------------------------------------------------------
% Load data from mat file.
s = load('data_compact.mat')
data_compact = s.data;
x = data_compact(:,1);

% Plot data.
plot(x, data_compact(:,2), 'b-');
xlim([x(1), x(end)]);
grid on;
hold on;

%--------------------------------------------------------------------------------------------------
% Smooth with a savitzky-golay filter.  Polynomial order = 2, window width = 351 elements.
smoothY = sgolayfilt(data_compact(:, 2), 2, 351);
plot(x, smoothY, 'r-');

%--------------------------------------------------------------------------------------------------
% Find peaks.  Must be separated by 13000 elements.
[peakValues, indexesOfPeaks, widths, proms] = findpeaks(smoothY, 'MinPeakDistance',13000); % peaks
% Remove an occasional outlier that is below the midpoint.
meanSignal = mean(smoothY);
outlierIndexes = peakValues < meanSignal;
peakValues(outlierIndexes) = [];
indexesOfPeaks(outlierIndexes) = [];
% Plot peaks.
plot(x(indexesOfPeaks), peakValues, 'g.', 'MarkerSize', 30);

%--------------------------------------------------------------------------------------------------
% Find Valleys.  Must be separated by 13000 elements.
[valleyValues, indexesOfValleys] = findpeaks(-smoothY, 'MinPeakDistance', 13000); % valleys
valleyValues = -valleyValues; % Make upright again.
% Remove an occasional outlier that is above the midpoint.
outlierIndexes = valleyValues > meanSignal;
valleyValues(outlierIndexes) = [];
indexesOfValleys(outlierIndexes) = [];
% Plot valleys.
plot(x(indexesOfValleys), valleyValues, 'c.', 'MarkerSize', 30);
message = sprintf('Found %d peaks, and %d valleys', length(indexesOfPeaks), length(indexesOfValleys));
title(message, 'FontSize', fontSize);

% Maximize the figure window.
g = gcf;
g.WindowState = 'maximized'

fprintf('%s\n', message);
uiwait(helpdlg(message));
fprintf('Done running %s.m ...\n', mfilename);

[Jay Vaidya]

Hey thanks, it works. It would be great if you can remove the data files from both your messages because the problem is solved.

[Walter Roberson]

The data is part of the question, and the question loses meaning without the data. https://www.mathworks.com/matlabcentral/answers/696995-find-peaks-valleys-of-a-noisy-signal#comment_1215630

[Jay Vaidya]

I understand, but can you then only keep the data set (column 1 and 2) instead of the all columns? Rest of the columns are not a part of the question. I hope this is fine at least.

[Image Analyst]

OK, post it for me and I'll replace it. However, like Walter said, no one has any idea what this data represents, much less the other columns, so I don't think you need to worry about leaking any proprietary/secret information. And I do think it's a nice example of how to filter noisy data to find peaks in the presence of noise.

[Jay Vaidya]

Ok, thanks. Here it is. Please replace this file in both the posts with your older attachments.

[Image Analyst]

Done.

Answer 2

[Image Analyst]

If there is noise on your peaks, have you tried sgolayfilt() with order 2 or 3? It's in the Signal Processing Toolbox.

[Jay Vaidya]

No, I have not. Let me see that.