Does phase distortion affect Discreet Fourier Analysis? - Page 1
Forum section: electronics / beginners

author: Silenus
author_rank: Contributor
timestamp: November 29, 2015, 08:10:01 pm
content: Hey guys,Bit of a mathy question here. I am looking at implementing a filter to process some mixed frequency data with the end result being a decomposition of the data using discreet Fourier transform into the frequency components. When designing a filter, the phase response of the system has to be considered in case it is non-linear (which is most likely is) which causes phase distortion in the non linear regions of the phase response. Now, from my understanding, a non-linear phase response will simply shift different frequencies by different amounts without changing the fundamental frequency components. Does that mean that a Fourier transform of a signal that passed through a linear-phase response would be the same as if it were passed through a non-linear phase response? In other words, if I just want to perform a Fourier analysis on the filtered waveform, do I have to worry about phase distortion at all?

author: TimFox
author_rank: Super Contributor
timestamp: November 29, 2015, 09:30:05 pm
content: The non-linear phase response will shift the phase of each discrete (indiscreet) frequency component in the spectrum, but will not affect the magnitude of each. If you are interested in only the power spectrum (technically, magnitude squared), there will be no effect.The actual Fourier transform of a real-valued waveform is complex (real and imaginary parts), and both are needed to invert the transform to recover the original waveform. The magnitude is the quadrature sum (root of real squared plus imaginary squared) of the two components.

author: bson
author_rank: Unknown
timestamp: November 30, 2015, 02:48:29 am
content: It won't affect the frequency or magnitude, but be aware that it will introduce group delay. This may be problematic if your sample set is short in duration since the delayed part of the spectrum can get pushed outside it. More specifically, for due diligence, measure the phase response and estimate the group delay based on the slope (or if it's a VNA that can estimate it just use that) and then figure the number of trailing samples you need to make sure you're not missing anything. (But this is really of no real concern except for very short sample durations relative to the bandwidth of the signal.)

author: jeffsf
author_rank: Contributor
timestamp: November 30, 2015, 07:06:37 pm
content: Quote from: Silenus on November 29, 2015, 08:10:01 pmYes, if you care about anything more thanpowerin each frequency bin.if you have a non-linear phase response, the phase of the various components will be changed relative to each other in a way that doesn't look like a simple time delay. Thefrequenciesthemselves aren't changed, but the phase relationship between them are.There is a lot of material already out there for Fourier analysis and associated filter design. There are advantages and disadvantages to various kinds of filters for Fourier analysis, depending on what you are looking to accomplish.I'd look at Matlab or octave if you want to "play around" to understand how the various filters and discrete Fourier transform approaches for the kinds of signals you are working with.