# When is phase needed in DFT?

I observed than people often compute the DFT of a signal using FFT and just observe the peaks in the "modulus VS frequency" diagram (kind of a power spectrum density). Obviously only half of the information appears in this diagram and it is not possible to retrieve the original discrete signal from this plot only.

Question: In practice, in which cases is the "phase VS frequency" plot needed or not?

• Is your question only about plots? FFT phase results are required when using an FFT for filtering, such as in overlap-add/save fast convolution. Phase results are also required by algorithms that measure the phase difference between offset DFT windows, such as for phase vocoder analysis/resynthesis algorithms. Etc. Sep 19, 2016 at 22:04
• @hotpaw2 Well, not specifically plots, just phase in general. I have never seen people using FFT phase in mechanics, for example - this is probably because resonance phenomena, which are of intersest, appear in terms of modulus. The examples you give are exactly what I am looking for. E.g. to lowpass a signal, you cannot just cut the frequencies about a given threshold in the amplitude-freq. diagram, because of the phase, as you write. But I am not very comfortable with this... Sep 19, 2016 at 23:44
• In mechanics, phase vs. frequency can be very important in control systems, the difference between stable and unstable feedback (steam engine speed governors, etc) Sep 20, 2016 at 1:11
• phase is part of the mathematics of the DFT. sometimes we don't care about it, but often when phase is totally overlooked, something bad or undesireable happens. usually when drawing the result of the DFT, phase is ignored. but just in the sketching of the DFT output. Sep 20, 2016 at 3:00

## 1 Answer

From the perspective of filtering, a common LTI system will weight each components in the input signal: (1) weighting means changing the magnitude values (it is apparent in multiplication of two complex numbers), thus it is often to observe the magnitudes (this does not mean the phase is not important; (2) of course, phase information is also part of the whole signal, and although the phase information may be also changed, but the phase is not apparent; (3) we can consider a FIR filter, and compare the changes of both magnitude and phase.