# Phase shift using FFT

1. Oct 3, 2007

### marksayles

What I want to do is apply a frequency-independent phase shift to a Gaussian Noise signal. Obviously I can just invert it to get a pi shift. Also I can take the Hilbert transform to get a pi/2 shift and I can invert that to give myself in effect a 3/2pi shift. BUT..... what I want to do is to be able to apply any phase shift, 10, 20, 30 degrees etc.

The way I have been thinking about this is that I can take the FFT of the noise and get the magnitude and phase information, and then I could manipulate the phase but leave the magnitude the same and take the IFFT to get my phase-shifted signal. Here is an example bit of matlab code doing this on a single sinusoid. As it is here the code doesn't work. But if you change the phase shift p from pi/2 to pi then it does? Is there something I'm missing. Perhaps I need to apply the phase shift differently to the positive and negative parts of the FFT? Or is it something to do with the fact that theta is distributed on [-pi pi] and when I add "p" I change this and make it ambiguous or something?

sr=10000;
dt=1/sr;
len=0.5;
t=0:dt:len;
f=500;
%generate signal
sig=sin(2*pi*f*t);
%Define a phase shift in rads
p=pi/2;
%Get the FFT of the signal
z=fft(sig);
%Get the magnitude
mag=abs(z);
%Get the phase
theta=angle(z);
%Add the phase shift onto the phase
theta=theta+p;
%Set the new real and imag parts of the spectrum
R=mag.*cos(theta);
I=mag.*sin(theta);
%Make the new spectrum
spec=complex(R,I);
%Get the new signal
newsig=real(ifft(spec));
%plot the signals
figure;plot(t,sig);hold on; plot(t,newsig,'g');