DEMO_GABFIR Working with FIR windows
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:
1) 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.
2) 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.
Figure 1: Hanning FIR window
This figure shows the a Hanning window in the time domain and its
magnitude response.
Figure 2: Kaiser-Bessel FIR window
This figure shows a Kaiser Bessel window and its magnitude response,
and the same two plots for the canonical dual of the window.
Figure 3: Gaussian FIR window for low redundancy
This figure shows a truncated Gaussian window and its magnitude
response. The same two plots are show for the truncated canonical
dual window.
Figure 4: Almost tight Gaussian FIR window
This figure shows a tight Gaussian window that has been truncated
and its magnitude response.
Url: http://ltfat.github.io/doc/demos/demo_gabfir.html
See also: firwin, firkaiser, gabdual.
Package: ltfat