How to align multiple signals?

Hi Matlab experts,

I'm trying to align these signals but have yet to be successful.

The signals are attached. They are periodic, noisy sin signals. I used the alignsignals function as well as xcorr to align the signals. Could somebody help me out with that?

Moreover, how can I compute the frequency of these signals?

Thanks in advance!

Answer 1

[Sulaymon Eshkabilov]

Here is one of the viable solutions to compute resonant frequencies of each signal and find out if their are coherent:

S1 = load('s1.mat').s1;
S2 = load('s2.mat').s2;
S3 = load('s3.mat').s3;
S4 = load('s4.mat').s4;
S5 = load('s5.mat').s5;
S6 = load('s6.mat').s6;
fs = 1024;
S = [S1; S2; S3; S4; S5; S6];
N = length(S1);
freq = fs*(0:(N/2))/N;      % Freq values
for ii=1:6
Y = fft(S(ii,:), N);                % FFT of the signal s(t)
Yp = abs(Y/N);                   % Absolute value or magnitude of the signal spectrum
semilogy(freq,Yp(1:N/2+1), 'linewidth', 2) 
hold all
end
title('FFT analysis of a signal')
xlabel('Frequency, [Hz]')
ylabel('Magnitude of signal = |S(f)|')
ylim([0, 0.025])
legend({'s1', 's2', 's3', 's4', 's5', 's6'})
grid on

You can check signal coherences using wcoherence() function:

wcoherence(S1,S2)

wcoherence(S2,S3)

wcoherence(S3,S4)

wcoherence(S4,S5)

wcoherence(S5,S6)

It looks like signal s5 and s6 are pure noise.

[Susan]

@Sulaymon Eshkabilov Thank you so much for your response. I genuinely appreciate it.

Please tell me how I interpret the first figure's results regarding the relationship between the time domain signals.

I went through the wcoherence documentation but am still trying to figure out how to interpret the results. Any help on that would be greatly appreciated.

Finally, how should I do that if I want to align these signals in the time domain?

[Sulaymon Eshkabilov]

Most welcome. What do mean to align the signals in the time domain? Put them together or what? to make their peak values correspond?

You can try alignsignals() fcn:

[S2a, S3a] = alignsignals(S2, S3, [], "truncate");
nexttile
plot(S2), hold on
plot(S3)
nexttile
plot(S2a), hold on
plot(S3a)
hold off

See - DOC.

Answer 2

[Sulaymon Eshkabilov]

One fundamental question for signal processing is a "must", that is "what is the data sampling time or sampling frequency?"

Pl., provide this info.

[Susan]

@Sulaymon Eshkabilov Thanks for your response. The sampling rate of all signals equals 1024.