Find similarities between two signals

I'm trying to find similarities between my template signal and a lot of other signals. I have tried to use cross-correlation (xcorr) and also peak detection on the signals to find similarities between the template and the signals. The problem is that the algorithm for finding signals that are similar does not work as a want.

Below are my template signal (Figure 1)

and here is one signal that the cross-correltion fought were similar (Figure 2)

Although the two signals have similarities, figure 2 does not contain the high peaks as in figure 1. I want to find signals that contain those clear peaks. I have tried to solve this by using findpeaks with two conditions "MinPeaksHeights'' and "MinPeakDistance'’ to find those bigger peaks and exclude smaller peaks. Somehow it still manages to sometimes find peaks and similarities between signals that does not look similar and I don't really know why.

Is there a better way to find the same peak characteristics as the template?

Below are the part where I try to perform the algorithm to identify similar signals to the template:

template = (template - mean(template)) / std(template);
signal_normalized = zscore(signal, [], 1); % Normalize along time axis


% Define correlation threshold for component selection
correlation_threshold = 0.4; 
matching_components_indices = [];

for k = 1:size(signal, 2)
    % Calculate cross-correlation with the template
    correlation_with_template = max(xcorr(template, signal_normalized(:, k), 'coeff'));
    
    % Check if correlation is above the threshold
    if correlation_with_template > correlation_threshold
        matching_components_indices = [matching_components_indices, k];
    end
end

% Sets amplitude threshold for peak detection
amplitude_threshold = 25; 
min_peak_distance = 100; % Min distance between peaks
% Find peaks in the matching components
selected_components_indices = [];
for k = 1:length(matching_components_indices)


    [pks_pos, locs_pos] = findpeaks(signal(:, matching_components_indices(k)), ...
                                     'MinPeakHeight', amplitude_threshold, ...
                                     'MinPeakDistance', min_peak_distance);
    
    [pks_neg, locs_neg] = findpeaks(-signal(:, matching_components_indices(k)), ...
                                     'MinPeakHeight', amplitude_threshold, ...
                                     'MinPeakDistance', min_peak_distance);
                                 
    % Combine positive and negative peak locations
    pks = [pks_pos; pks_neg];
    locs = [locs_neg; locs_pos];
    % Check if any peak exceeds the threshold
    if length(pks) > 2
        selected_components_indices = [selected_components_indices, matching_components_indices(1)];
        found_signal(:,m) = signal(:, selected_components_indices(1));
        m = m + 1;
    end

Maybe I can improve the peak detection part?

Thanks for any help. If I was unclear, let me know

[Chunru]

try "detrend" before xcorr.

[Star Strider]

With respect to findpeaks, using 'MinPeakProminence' is usually successful at returning the peaks, and should work even with a non-zero baseline.

[Gus]

@Chunru Thanks, I tried using "detrend" which gave me better results, but it did not improve the detection of similarities good enough.

[Gus]

@Star Strider Thanks for the reply. The problem with "MinPeakPromience" is that some peaks it finds have similar peaks (amplitude) but not always similar shape of the peak structure, if you know what I mean. The peaks I am looking for always have similar "uphill" as "downhill" (from the peaks perspective), they have similar slopes that is. I thought maybe it's possible to calculate the derivative of the curve of both the "uphill" and "downhill", and then only look for those kinds of derivative near peaks when looking at other signals to find similarities in peaks?

[Star Strider]

My pleasure!

It might be necessary to filter the data first, probably with a lowpass filter to eliminate the high-frequency noise. (A bandpass filter would probably eliminate the baseline drift as well, so consider that option if that is the result you want.)

You can determine the optimal frequencies for the filter you choose (if that is what you want to do) by taking the fft of both signals (since you will want to use the same filter for both), and then desiging the filter appropriatel using that information. This also assumes both signals have the same sampling frequency, as they must for this sort of approach.

Answer 1

[Constantino Carlos Reyes-Aldasoro]

Perhaps this file exchange analysing an ECG signal can give you some ideas:

https://uk.mathworks.com/matlabcentral/fileexchange/68246-visualization-and-analysis-of-an-electrocardiogram-signal?focused=7fbc0610-5e23-435e-a271-ddd80d1065d0&tab=example

[Gus]

Thanks, I will look into it.

Answer 2

[Image Analyst]

The question is really what kind of metric(s) would be useful for you?

How about RMS difference? rms

How about mean absolute deviation or median absolute deviation: mad

How about just locating peaks and finding the distance between peaks of the test signal to the reference signal? findpeaks

How about the correlation coefficient? corrcoef

Are the signals aligned already because some of those metrics need the signals to be aligned if you want to compare the shape of the signal. Or they might be a good metric of how misaligned they are.