# Phase of FFT

1. May 7, 2012

### evawoo

Hey all,

I'm new here.
Currently I'm struggling with the phase of FFT. I read that the phase of FFT is relative to the start of the time domian signal. In my measurement I recorded a signal which is a sinus sweeping from 100hz to 3000hz. after FFT i obtained a phase spectrum within the specified frequency range. what I dont get is how do we get for each frequency component a phase if the phase of fft related only to the start time. How does the phase is transformed from the time domain to the frequency domain.. I would really appreciate if some of you guys provide me an explaination regarding to this.

cheers,
Eva

2. May 7, 2012

### PhilDSP

Hi Eva, Welcome to the forum!

The FFT basically performs an integration operation over the time period of the signal. It does that by taking the inner product of each frequency component with the signal over the length of the signal (or length of each data window).

So the starting point of signal side of the inner product is synchronized with the starting point of the frequency component-analysis side of the inner product (which is common for each frequency component). The results of that is that the phase reference (of each frequency component) is locked to the beginning of the signal. Is that clear enough?

3. May 7, 2012

### evawoo

Hi Phill,

Thanks a lot for the fast reply. That was really impressive. But I still unable to explain the following phenomenon occuring to my measurement results. I characterized an acoustic system by taking a complex TF (transfer function：frequency response of an output/frequency response of an input) of the system. the amplitude of the TF gives peaks at resonance frequencies, which is clear. because the resonance frequency is frequencies at which the system has the strongest osillation. In the phase vs. frequency plot, I observed that the phase decrease from -50deg to -180deg as the frequency increases to the resonance frequency, and then directly jump to 180deg at the resonance frequency. So it seems that I could obtain the resonance frequency by the phase shift too. But I cant explain the physical mechanism behind this. It would help me a lot if you could explain that to me, thanks

best,
Eva

4. May 7, 2012

### PhilDSP

I'm a bit rusty on the details of that but I think for very sharp filters the phase will reverse in a tight frequency range. We could probably expect the same thing to happen in a material that is responding acoustically with a strong resonance. If you can sample the signal at a higher time resolution you should get a higher resolution in the frequency domain and may be able to see a slight slope for the phase reversal.

5. May 7, 2012

### evawoo

Hi,

Thanks a lot for that.

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