where, is the sampled frequency response of a filter with impulse response
Let's examine the result this has on the signal in the time domain:
We see that the result is convolved with a windowed version of the impulse response . This is in contrast to the OLA technique where the result gave us a windowed filtered by without the window having any effect on the filter, provided it obeys the COLA constraint and sufficient zero padding is used to avoid time aliasing.
In other words, FBS gives
while OLA gives (for )
- In FBS, the analysis window
smooths the filter frequency response by time-limiting the corresponding impulse response.
- In OLA, the analysis window can only affect scaling.
Time Varying Modifications in FBS
Constant-Overlap-Add (COLA) Cases