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I would like to find the phase variations of the signal with respect to time axes:

S = sin(2*pi*100*t + pi/4) + cos(pi*500*t) + sin(2*pi*100*t + 5*pi/2);

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My attempt to get the phase, see figure below:

enter image description here

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  • $\begingroup$ using fft only frequency content of the sin and cos components are estimated neglecting the phases. I want even the phase information of the components, please help me $\endgroup$
    – Shaheena
    Feb 6 '20 at 11:46
  • $\begingroup$ This would apply if the equation was of the form of cos(a)+j sin(b). There is no j so there is no phase other than 0 and pi (it is a real signal!) $\endgroup$
    – Dan Boschen
    Feb 7 '20 at 4:09
  • $\begingroup$ @jomegaA I want to plot the phase variations along the time series i.e x axes is time and y axes is phase, where as in the above figure the variations are w.r.t frequency. we observe 3 phase changes in the time window between 0 to 0.02 window in time domain and is periodic. $\endgroup$
    – Shaheena
    Feb 7 '20 at 4:53
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This is a real signal, so the phase can only be $0$ to $\pi$.

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  • $\begingroup$ what is actually the angle(fft(S)) giving? $\endgroup$
    – jomegaA
    Feb 7 '20 at 8:54
  • $\begingroup$ angle(fft(S)) gives the phase variations in the frequency domain but I need phase variations in time domain like for example, in phase-modulated signal I want to detect the phase changes occurring at different time instances. $\endgroup$
    – Shaheena
    Feb 7 '20 at 9:06
  • $\begingroup$ @Shaheena Please define what you are referring to as "phase variation". In my definition you would need to have a complex signal to have any phase results other than $0$ o $pi$; the arg expression in MATLAB and Octave is consistent with this--it returns the phase versus time and for your signal would be $0$ or $pi$ only. $\endgroup$
    – Dan Boschen
    Feb 7 '20 at 12:08

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