Editing Spectrogram (section)

==Limitations and resynthesis==
From the formula above, it appears that a spectrogram contains no information about the exact, or even approximate, [[Phase (waves)|phase]] of the signal that it represents. For this reason, it is not possible to reverse the process and generate a copy of the original signal from a spectrogram, though in situations where the exact initial phase is unimportant it may be possible to generate a useful approximation of the original signal. The Analysis & Resynthesis Sound Spectrograph<ref>{{cite web|url=http://arss.sourceforge.net|title=The Analysis & Resynthesis Sound Spectrograph|website=arss.sourceforge.net|access-date=7 April 2018}}</ref> is an example of a computer program that attempts to do this. The [[pattern playback]] was an early speech synthesizer, designed at [[Haskins Laboratories]] in the late 1940s, that converted pictures of the acoustic patterns of speech (spectrograms) back into sound.

In fact, there is some phase information in the spectrogram, but it appears in another form, as time delay (or [[group delay]]) which is the [[Dual (mathematics)|dual]] of the [[instantaneous frequency]].<ref name="Boashash1992">{{cite journal | last=Boashash | first=B. | title=Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals | journal=Proceedings of the IEEE | publisher=Institute of Electrical and Electronics Engineers (IEEE) | volume=80 | issue=4 | year=1992 | issn=0018-9219 | doi=10.1109/5.135376 | pages=520–538}}</ref>

The size and shape of the analysis window can be varied. A smaller (shorter) window will produce more accurate results in timing, at the expense of precision of frequency representation. A larger (longer) window will provide a more precise frequency representation, at the expense of precision in timing representation. This is an instance of the [[Heisenberg uncertainty principle]], that the product of the precision in two [[conjugate variables]] is greater than or equal to a constant (B*T>=1 in the usual notation).<ref>{{Cite web |url=http://fourier.eng.hmc.edu/e161/lectures/fourier/node2.html |title=Heisenberg Uncertainty Principle |access-date=2019-02-05 |archive-date=2019-01-25 |archive-url=https://web.archive.org/web/20190125182117/http://fourier.eng.hmc.edu/e161/lectures/fourier/node2.html |url-status=dead }}</ref>