Is there any relation between FFT size and phase error? (as for amplitude)

[Terminator3]

It is well known, that when analysed signal frequency appears between FFT frequency bins, it gets "sidelobes". Then frequency peak amplitude have some error. What about phase? Can we improve phase measurement by increasing FFT size? I think it is correct for analyzing single signal. But when we use relative measurements, this error dissapears because of substraction (for example, in all kinds of FFT phase interferometers). Are my conclusions right?

 

[MagicianT]

Can we improve phase measurement by increasing FFT size? I think it is correct for analyzing single signal.

You can't fix an error introduced by frequency "offset" using bigger fft size. Actually, you make it worse, as bigger fft size has better frequency resolution and consequently more susceptible to "offset". I'm referring in offset between sampling frequency (Fs) and Freq. of interest (Fi) in input data pull.
Options #1 - change sampling rate to be exact multiple of the Fi, Fs = N x Fi.
Options #2 - do a "windowing" - Hamming , Hann, etc.

But when we use relative measurements, this error dissapears because of substraction (for example, in all kinds of FFT phase interferometers). Are my conclusions right?

Correct, offsetting error due mismatch Fs and Fi, when Fs = N.d x Fi, where N.d is not an integer number, would be equals in both channels - assuming their sampling rate also equals, and differential value would be proportional only to absolute phase offset, like in case different TOA.

 

[Terminator3]

How to choose FFT size when we measure phase difference? For constant differences in phase FFT size is bigger, for changing over time phase differences FFT seems must be smaller size. But it is unclear how it will affect phase difference measurement. Maybe it does not depend on FFT size at all, and in case of big FFT's we only get bigger "time lag" for changing phases, and no improvement on constant phase signals? For example we have one frequency signal, and two channel phase difference goes from 90deg to 0deg for time period of 100ms. How it affect error in measurements if we take FFT's each 1ms, 2ms or say 10ms bins. FFT's can be taken from sliding window each 1 ms.

 

[KlausST]

Hi,

your application is not clear to me.

you want to measure phase difference.
The FFT shows the phase of a single signal referenced to the sample array.

For two signals you can calcualte phase difference if you use two <b>synchronously</b> sampled signal data arrays (FFT input)


Klaus

 

[FvM]

I see two much guessing and too little profound calculation by Terminator3.

You can easíly see that a FFT window (either smoothed or rectangular) which length is not an integer multiply of the input signal period involves a systematical phase error. The amount can be calculated for specific parameters.