The input signal is complex conjugate, but the IFFT output is complex!

The input data are amplitude (Ax) and phase (phase2) vectors used to construct the frequency spectrum (Xk), and then restore its real signal by IFFT.

The amplitude spectrum exhibits even symmetry and the phase spectrum odd symmetry, then ifft should give back a real value signal.

However, the ifft results to a complex series.

What is the problem on this code?

Thanks a lot!

Answer 1

[David Goodmanson]

Hello yz,

The problem is that to produce a real ifft, the first element of Ax, which is the f=0 term, has to be real since that term produces the dc offset in the time domain, which is real. The nyquist term, with index N/2+1,must also be real. In the code below I just inserted a couple of zeros after the fact instead of doing it right, but you get the idea.

Ax =[323 99 4.7 0.24 0.047 0.0045 4.7e-12 ...
     0.0045 0.047 0.24 4.7 99]; %The amplitude specturm is even symmetry    
Nx = length(Ax);
phase1 = pi*randn(1,Nx/2+1); %The one-side phase value is generated randomly.
phase2 = [phase1 -(phase1(Nx/2:-1:2))];% construct the two-side phase spectrum which is odd symmetry 
phase2([1 Nx/2+1]) = 0; %                                       <----
Xk = Ax.*exp(1j*phase2); %construct the frequency spectrum      
F_rec = ifft(Xk)
max(abs(imag(F_rec)))       % should be tiny

[yang zhang]

Thanks very much for your guide! It works now!