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From: Shaddy on 16 Nov 2009 13:22
I am trying to write a simple example to test the time shift property of FFT.
I have two problems which I hope that someone can help me with.

Here is the program I wrote:

close all;
clc;
clear all;


T=1; %% period
A=1; %% Amp.
N=2^15; %% number of points
w=2*pi/T;

t0=.4; %% Time Shift
t=linspace(0,2*T,N);
dt=t(2)-t(1);
Fs=1/dt; %% Sampling frequency
f = Fs*linspace(0,1,N);

y1=A*sin(w*t); %original function in time
Y1=fft(y1); %convert to Freq domain
y1shifted=ifft(Y1.*exp(-2*pi*i*t0*f)); % Linear phase shift in
%%freq domain convert back to time domain


figure;
subplot(2,1,1)
plot(t,y1,'b')
grid on
xlim([min(t) max(t)])
ylim([-A A])
title('Original Function sin(t)');
ylabel('t')

subplot(2,1,2)
plot(t,y1shifted,'r')
grid on
xlim([min(t) max(t)])
ylim([-A A])
title('Shifted Function sin(t-t_0)');
ylabel('t')


1)
I keep getting the following error msg,:
'Warning: Imaginary parts of complex X and/or Y arguments ignored'
and the plot does not look as I may expect it to be.

When I replace the linear phase shift in freq domain and converting back to time domain to :
y1shifted=ifft(Y1.*exp(-2*pi*i*t0*f),'symmetric'); % Linear phase shift in
%%freq domain convert back to time domain

Can someone explain to me why is that?

2)
When I change the t to
t=linspace(0,2.3*T,N);
I gets a weird behavior at the beginning of the pot. Why?

Thank you
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