ifft output is complex?

I have a time series (x). I have taken the fft of the time series (X). I want to shift the entire series, or in the future only certain frequency components, by phase shift (theta). I have changed the complex numbers of X to alter the angle whilst conserving the abs(X). I then ifft the output (X2) and I get a complex output and im not sure why?

Thanks

if true

     for m=2:length(X)
        n=X(m);
        r=real(n);
        im=imag(n);
        a=angle(n);
        a2=a+pi/2;
        r2=(r*cos(a2))/cos(a);
        im2=tan(a2)*r2;
        z=complex(r2,im2);
        X2(m,1)=z;
      end
  output=ifft(X2);

Answer 1

[Dimitris Kalogiros]

After the manipulations of fft values X , If abs(X) exhibits even symmetry and angle(X) odd symmetry, then ifft should give back a real value time sequence. Otherwise, ifft results to a complex time series.

Answer 2

[Matt J]

Shifting the angle by a constant amount for every frequency component will not translate the signal. The translation t0 has to be linearly weighted by frequency.

Also, it is much easier to implement what you have done just by doing,

output=ifft( X.*exp(-j*2*pi*f*t0) )

[ben howey]

where f has units of Hz and t0 is a phase shift in radians?

[Matt J]

t0 is a time shift in seconds.

[ben howey]

So is there no way to phase shift components of the spectrum by a given phase angle? i.e taking the component at 0.3 Hz and adding a pi/2 phase shift to make that component z=sin(2*pi*0.3+pi/2)

[Matt J]

I think you mean z=sin(2*pi*0.3*(t+pi/2)) ?

[ben howey]

*sorry z=sin(wt+pi/2) = sin(2*pi*0.3+pi/2) , where w is omega frequency in rad/s

[Matt J]

That is the same as

 z=sin(2*pi*0.3*(t+1/1.2))

So yes, it is possible. You would add +/- 1/1.2 to the phase angle of the spectral components at +/- 0.3 Hz.