Compare same frequency components of two signals

Hello,

I have two signals and I want to split each one of them in same number of components. After that, I want to find the components with the (almost) same frequency and compare their plots.

Any idea how could I find same frequency components of the signals?

Thanks.

Answer 1

[TED MOSBY]

Hi,

To compare same frequency components of two signals, you can follow the 3 steps below:

1. Decompose each signal into the same number K of narrow-band components:

MATLAB's function "emd" returns intrinsic mode functions "imf" and residual signal "residual" corresponding to the empirical mode decomposition. You can use "emd" to decompose and simplify complicated signals into a finite number of intrinsic mode functions:

K  = 6;                 % how many modes you want
[imf1,~] = emd(x1,'MaxNumIMF',K);   % x1  : first signal
[imf2,~] = emd(x2,'MaxNumIMF',K);   % x2  : second signal

2. Extract a representative frequency for each component:

Dominant frequency = peak of the power-spectral density (PSD) of that component:

function f = dominantFreq(sig, fs)
    %% Return the dominant frequency (peak of one‑sided PSD) in Hz
    nfft = 2^nextpow2(numel(sig));
    xdft = fft(sig, nfft);
    psd  = abs(xdft(1:nfft/2+1)).^2;
    fvec = (0:nfft/2)' * fs / nfft;
    [~, idx] = max(psd);
    f = fvec(idx);
end

3. Pair components with “almost the same” frequency:

"pairs" tells you which IMF in "x1" matches which IMF in "x2". If you want an automatic global matching, MATLAB’s "matchpairs" can find the optimal one-to-one assignment that minimises total frequency error:

tol = 0.05;            % 5 % relative tolerance

pairs = [];            % rows: [idxSignal1   idxSignal2]
for k = 1:K
    [d, j] = min( abs(dom2 - dom1(k))./dom1(k) );    % relative diff
    if d < tol
        pairs = [pairs; k  j];
    end
end

You can now go ahead and plot the matched pairs.

Below is the documentation of MATLAB functions used above:

• "emd" : https://www.mathworks.com/help/signal/ref/emd.html?s_tid=doc_srchtitle
• "fft" : https://www.mathworks.com/help/releases/R2025a/matlab/ref/fft.html?s_tid=doc_srchtitle#d126e528545
• "matchpairs" : https://www.mathworks.com/help/matlab/ref/matchpairs.html?s_tid=srchtitle_support_results_1_matchpairs

Hope this helps!

[Christine Tobler]

matchpairs is part of core MATLAB, not the optimization toolbox. It's also not used in the code shown here?

[TED MOSBY]

Yeah i just gave matchpairs as another option, and yes I mistook it for that toolbox, have edited the answer!