Adding Random phase causes fft anomalies?

Question

Nathan Kennedy 2017-12-14

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https://ww2.mathworks.cn/matlabcentral/answers/372955-adding-random-phase-causes-fft-anomalies

回答： Joel Miller 2017-12-14

Hi

If I add random_phase to my waveforms then the fft goes skewy - basically it breaks down and is not producing what it should be like when random_phase is not present in sinewave generation loop.

%Setup sampling times and frequency range
f=(20.2 : 0.1 : 21.1)*10^9;
Fs = 3*max(f);
Ts = 1/Fs;
end_t = 0.5*10^-6
dt=0: Ts : end_t -Ts
a=0; b=pi; %for random phase calculation
%Below part adds a new sine wave every 0.01*10^9 within frequency range
for a=1:length(f)-1
random_phase = (b-a).*rand(1,length(dt))+a;
y(a,:) = 5*sin(2*pi.*f(a) .* dt + random_phase);  %remove random_phase and scripts works fine. 
end
%combined waveform
waveform = sum(y);
%setup frequency domain for FFT
N=length(waveform);
freq_domain = (0:N-1);
freq_domain = f_domain*Fs/N
ft=2*abs(fft(waveform)/N);
figure(1)
bar(freq_domain, ft);
ax=gca; ax.XAxis.Exponent = 9;
xlim([20 *10^9 21.4*10^9]);

Completely stumped how random phase messes up my fft...

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Answer 1

Star Strider 2017-12-14

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在 MATLAB Online 中打开

The random phase will shift your sine curve randomly in time, essentially destroying the periodicity. You can see this easily if you plot your signal in the time domain:

figure(2)
plot(dt, waveform)
grid
subplot(2,1,2)
plot(dt, waveform)
axis([0  2E-8    ylim])
grid

Also, if you use plot rather than bar, the Fourier transform is easier to see.

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Answer 2

Joel Miller 2017-12-14

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If you are trying to randomly shift the phase of the sinusoids, sin(2*pi.*f(a) .* dt), then random_phase should be a scalar. When random_phase is a vector of length dt, you are adding a different phase to each time increment of the sinusoid. That is a reasonable definition of random (phase) noise. You can see this by fourier transforming just random_phase.