STFT multiplied with Gaussian window vs STFT multiplied by rectangular window I am currently analysing my signal by looking at its spectrogram to determine the sinusoidal frequency content at the local sections of my signal overtime. I can do my spectrogram in 2 ways:


Directly get the FFT of each local sections. Same as I multiply each section by a rectangular window with a height 1 and get the FFT.
Multiply each section by a Gaussian window and get the FFT.


Apparently, I get 2 different pictures of my spectrogram. Number 2 is known as the Gabor Transform.

My question here is, what is the motivation for doing the Gabor Transform vs directly doing the FFT at each section of a signal?
Using a Gaussian window has one advantage over all other windows-- it yields the most compact time-frequency view of the spectrum. In other words, the product of the uncertainty in the time and frequency domains is minimized. This is due to the uncertainty principle of the Fourier transform. 

Incidentally, in physics this property of the Fourier transform is the mathematical underpinning behind the Heisenberg uncertainty principle, which states that the position and momentum cannot simultaneously be known to infinite precision. Replace "position" with "time" and "momentum" with "frequency" in that statement and you can see how this applies to spectral analysis. 

(There are other reasons not to use a Gaussian window as well, depending on what your application requires.)

Also, incidentally, Gabor was a physicist who first applied many mathematical tools from physics to signal processing problems, such as the analytic signal representation. It would not surprise me if his use of the Gaussian window in signal processing was carried over from quantum mechanics.