This demo demonstrates how to work with FIR windows in Gabor systems.
FIR windows are the windows traditionally used in signal processing. They are short, much shorter than the signal, and this is used to make effecient algorithms. They are also the only choice for applications involving streaming data.
It is very easy to compute a spectrogram or Gabor coefficients using a FIR window. The hard part is reconstruction, because both the window and the dual window used for reconstruction must be FIR, and this is hard to obtain, if the window is longer than the number of channels.
This demo demonstrates two methods:
- Using a Gabor frame with a simple structure, for which dual/tight FIR windows are easy to construct. This is a very common technique in traditional signal processing, but it limits the choice of windows and lattice parameters.
- Cutting a canonical dual/tight window. We compute the canonical dual window of the analysis window, and cut away the parts that are close to zero. This will work for any analysis window and any lattice constant, but the reconstruction obtained is not perfect.