Adding Random phase causes fft anomalies?

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Nathan Kennedy
Nathan Kennedy 2017-12-14
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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采纳的回答

Star Strider
Star Strider 2017-12-14
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.

更多回答（1 个）

Joel Miller
Joel Miller 2017-12-14
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.

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