Why phase information is usually ignored after Fourier transform?

Question

Why phase information is usually ignored after Fourier transform?

I have read in a tutorial [ref: FFT Tutorial] that interpretation of phase is usually challenging, so scientists do not show it or use it for their analysis. I would like to know when one can confidently ignore phase information without losing key information in his/her judgements.

Answer 1

Simply put:

• Because in interesting cases, it remains difficult to interpret, and people tends to use other tools
• Yes, potentially a lot of non-stationary features, timings, onsets, discontinuities

For a basic use, like measuring the relative energy of different frequency component, the phase is of little use. As waves tend to last over several samples, sliding/overlapping versions can help retrieving timing/localization of features.

However, phase contains a lot on information, especially on images, and perhaps plays an important role on perception (e.g. The importance of phase information for recognizing natural images). The importance of phase is recognized in many works, see for instance The Importance of Phase in Image Processing, and it is still an active topic. Multiscale phase might detect onsets, contours, while the distribution of phase coefficients could be used for texture retrieval. The phase computed is wrapped between $-\pi $ and $\pi $, and unwrapping it in 2D or 3D seems to remain challenging. Hence, some resort to complex transformations that are more localized than Fourier bases, like filter banks or "wavelets", to capture phase information at the correct scales.

Answer 2

Phase is used or not used depending on whether it is useful or not, whether "challenging" to some scientists or not.

Random opinion: In some domains, for instance cheap monophonic audio reproduction, most human listeners can't detect changes in spectral phase of many sound types (anywhere nearly as well as changes in spectral magnitude), so phase information could be ignored in certain types of analysis or processing, and yet still allow useful results (especially before the era of cheap computing power).

However in other audio domains, sonar imaging, beam steering, etc., phase is critical, and thus not ignored.

Random opinion: In other engineering domains, the transducers introduced so much uncalibrated phase distortion that computing the contaminated phase results didn't provide much useful information (perhaps until better calibrated measuring systems where invented/designed).