How to extract the correct phase of a sine wave from data

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Muhammad - 2020-11-30T10:12:07+00:00
Question: How to extract the correct phase of a sine wave from data

I'm trying to write a code which allows me to determine the phase of a sine wave from its vector. given: the sinusoidal  signal vector, its frequency unknown: its phase I have tried with this code but i don't understand why do i end up getting wrong/ unprecise results a=0; b=800; %time intervalls N=20000; %N number of samples t=linspace(a,b,N); %time vector ts=(b-a)/N; %sampling time fs=1/ts; %sampling frequency fn=fs/2; %Nyquist frequency fx=1; phix= 180; %Frequency and phase of x(t) x=sin(2*pi*fx.*t+phix* (pi/180)); %Original signal binwidth = 1 / (b-a); % frequency binwidth in Hz f_index = fx / binwidth +1; % frequency index y = abs(fft(x)) / (N/2); phase = angle(fft(x))* 180/pi+90; disp(phase(f_index)); for example here i get 187.2000 instead of 180 I'd be very grateful for your help and clarifications!

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    • Expert Answer

    Profile picture of Prashant Kumar Prashant Kumar answered . 2025-11-20

    The reason you get imprecise results is because you are using discrete fourier transform. When you get the phase of the frequency bin from fft, you get, roughly speaking, the phase of a frequency bin, but not the phase of a single frequency. You can get much better estimation if you analyse a few neighboring bins, but that’s a complex process.
    If you’d like to compute exact phase and you know the signal is exactly sinusoidal, you’d better just use asin(x(1)).


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