Rectangular mask short-time Fourier transform


In mathematics, a rectangular mask short-time Fourier transform has the simple form of short-time Fourier transform. Other types of the STFT may require more computation time than the rec-STFT.
Define its mask function
We can change B for different signal.
Rec-STFT
Inverse form

Property

Rec-STFT has similar properties with Fourier transform
  1. When
  2. When
If,and are their rec-STFTs, then
From the image, when B is smaller, the time resolution is better. Otherwise, when B is larger, the frequency resolution is better.
We can choose specified B to decide time resolution and frequency resolution.

Advantage and disadvantage

Advantage
The instantaneous frequency can be observed.
Disadvantage
Higher complexity of computation.
The rec-STFT has an advantage of the least computation time for digital implementation,
but its performance is worse than other types of time-frequency analysis.