from time domain to frequency domain and back to time domain

Hi to everybody,

I am trying to jump from a frequency response to an impulse response and I need to start from sth basic so I understand how it works.

Can someone please help me understand why the last plot doesn't look like the first (the one that is commented out in the code) one? I would expect them to be the same.

% N=100000; % the number of data points
% fs=44100; % sample rate, number of samples per second
% dt=1/fs;% time increment (in seconds per sample)
% t=dt*(0:N-1); % time domain (in seconds)
% fc=100; % carrier frequency
% x=sin(2*pi*fc*t); % sine
% figure()
% plot(t,x)

%spectrum
X=fftshift(fft(x)); % DFT and shift center to zero
df=fs/N; % the frequency increment
f=-fs/2:df:fs/2-df; % create the frequency axis
figure()
plot(f,abs(X))

% reverse procedure
y=ifft(X); % inverse fft
N2=length(X); % determine the length of the signal
dt2=1/fs; % determine the time increment
tim=0:dt2:(N2-1)*dt2; %create the time axis
figure()
plot(tim,y)

Answer 1

[Dr. Seis]

Your "X" has shifted the zero frequency amplitude to the center. You need to use ifftshift to get it back where Matlab expects... i.e.:

y = ifft(ifftshift(X));

[Dr. Seis]

P.S. I will look at your other problem in more detail when I have a little more free time tonight.

[buscuit]

sure, Elige. Thank you very much for the help so far.

[Kacper Muszynski]

Thank you very much for this, was stuck on it for the longest time. However, the signal I get appears to be shifted by pi/2, any ideas?

clear all;
clc;

n = -8*pi:0.01:8*pi;
x1 = 2*sin(2*n);            

subplot(3,1,1); plot(n,x1,'-b'), grid on,axis([-8*pi 8*pi -2 2]);

L = length(x1); 
X = fft(x1,L); 
X_amp = abs(fftshift(X)); 
w = linspace(-pi,pi,L);

subplot(3,1,2), plot(w/pi, X_amp), grid on;

x2 = X_amp;
x2 = ifft(ifftshift(x2)); %shift back from centre
x2 = fftshift(x2);

subplot(3,1,3), stem(n,x2),grid on,axis([-8*pi 8*pi -2 2]);