Finding the frequency and the phase shift of a Sin signal

Hallo,

i have this sin function with damping discribed with the equation in the photo, the plot under it is my signal.

how can i claculate F0 and phi0 of my Signal?

Answer 1

[Star Strider]

One option is described in Curve fitting to a sinusoidal function and a version that could be more appropriate to your problem is How to filter noise from time-frequency data and find natural frequency of a cantilever?

The one change I would make to that code is to replace the ‘zci’ funciton with:

zci = @(x) find(diff(sign(x)));

since it is more robust.

Those routines will calculate the frequency, phase, and other parameters.

Another option of course is to use the fft function.

[Ahmad Badran]

thank you for helping

i tried to do it with fft() using the following code

% len = length(pendel_h_a);
% fs = 100; 
% n = 0:len-1;
% f = n*fs/(len-1);
% y = fft(pendel_h_a);
% plot(f,abs(y));
%phase = angle(y);

but i'm getting the freqeuncy and the phase as a vector and i'm not sure how to determin F0 and phi0

[Star Strider]

The peak frequency will have a phase associated with it.

Use the findpeaks function on the absolute value of the first half of the complex Fourier transform to determine the index (preferably), then use that index to retuen the appropriate phase using the angle function on that value of the complex Fourier transform vector.

Something like this —

t = ...;                                                                    % Time Vector
s = ...;                                                                    % Signal Vector
Ts = mean(diff(t));                                                         % Sampling Interval (Assumed To Be Constant)
Fs = 1/Ts;                                                                  % Sampling Frequency
Fn = Fs/2;                                                                  % Nyquiat Frequency
FTs = fft(s - mean(s));                                                     % Fourier Transform
Fv = linspace(0, 1, fix(numel(t)/2+1)*Fn;                                   % Frequency Vector
Iv = 1:numel(Fv);                                                           % Index Vector

[pks, locs] = findpeaks(abs(FTs(Iv)));                                      % Peaks & Indices (May require'MinPeakHeight' Or 'MinPeakProminence' For Best Results)
Phase = angle(FTs(locs))                                                    % Phase Angle At Peak
PeakFreq = Fv(locs)

It may be necessary to experiment with this to get the result you want.

[Ahmad Badran]

Thank you very much i set the number number of peaks to one and i think i got the wanted results

[pks, locs] = findpeaks(abs(FTs(Iv)),"NPeaks",1);                                      % Peaks & Indices (May require'MinPeakHeight' Or 'MinPeakProminence' For Best Results)
Phase = angle(FTs(locs));                                                 % Phase Angle At Peak
Phase0 = rad2deg(Phase)
PeakFreq = Fv(locs)

hope it's right

thank you again

[Star Strider]

As always, my pleasure!