# Why does a phase shift in the frequency domain not produce a time delay in the time domain?

Suppose I have an input signal which represents a vehicle front suspension response that has been measured using an accelerometer. It is seen that the measured rear suspension response is effectively just a time delayed version of the front suspension response and shifting the rear signal forward in time by the delay causes the signals to align rather well. The intention now is to simulate this rear suspension response without needing an accelerometer to measure it. Knowing the time delay between the two signals, I am trying to simulate the rear suspension response using a set of transfer functions that have been measured on the vehicle.

s1 is the front signal, s2 is the rear signal. s2sim is the rear signal that I want to simulate. h11, h12, h21 and h22 are the transfer functions used to try and simulate the rear signal. h11= a11/f1 where a11 is the acceleration measured at point 1 when a force is applied at point 1 and h12 = a12/f2 where a2 is acceleration measured at point 1 when force is applied at point 2 and so on. I am also looking at the phase information and making sure that the rear suspension response is replicated rather than the front suspension response.

S1=fft(s1);
Fop1= S1./(h11+(h12.*exp(-1j*w*timedelay)));
Fop2=Fop1.*exp(-1j*w*timedelay);
S2SIM=(h21.*Fop1)+(h22.*Fop2); % where Fop1 and Fop2 are the operational
% forces at the front and rear respectively
s2sim=ifft(S2SIM) % or real(ifft(S2SIM));


When I look at the phase information, it is nearly identical to the front suspension response rather than the rear and when i take the inverse fft and use the cross correlation to find out the time delay between s1 and s2sim in the time domain, it is seen that the time delay is 0 which means the signal hasn't been delayed so I am doing something wrong. Can anybody help me out here.

• the premise of the question is false. phase shift in the frequency domain does produce shifting in the time domain. – robert bristow-johnson Aug 31 '14 at 18:04
• I realize that a phase shift in the frequency domain should produce a shift in the time domain as well but in this case it doesn't seem to work so I posted the question hoping somebody can help me figure out what I'm doing wrong. – Varun Sep 1 '14 at 11:10
• well, without specific knowledge about "h11" and "h12" or "w", i dunno what you could be doing wrong. – robert bristow-johnson Sep 1 '14 at 23:22
• I am just looking into a similar problem and stumbled upon this: dsp.stackexchange.com/questions/509/… Are you sure there isn't a circular shift in the time-domain? – Nikolay Tsenkov Mar 17 '17 at 11:36