Next: THE CHIRPLET
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This paper is devoted to physical (intuitive) considerations of the chirplet
transform. It is organized as follows:
- We first introduce chirping analysis functions
which may be thought of as generalized
- We then generalize Gabor's use of the
Gaussian window for his tiling of the time-frequency plane.
This generalization gives rise to the
four-dimensional time-frequency-scale-chirprate (TFSC)
- We next consider non-Gaussian
analysis functions, giving rise to a five-dimensional
- We then consider the use of multiple analyzing wavelets/windows,
first to generalize Thomson's method of spectral estimation
to the TF plane, and then to further generalize this result
to the chirplet transform.
The multiple analyzing wavelets/windows
(which we call ``multiple mother chirplets'' when they are used
in the latter context) collectively
act to define a single ``tile''
in the TF plane, corresponding to each point in the
chirplet transform parameter space. Such a tile
has a true parallelogram-shaped TF distribution whose shape is
by the six 2-D affine parameters.
- We generalize autocorrelation and cross-correlation by
using the signal itself (or another signal) as a ``mother chirplet''.
In other words, we analyze the signal against chirped versions
of itself (or against chirped versions of another signal).
- Finally, we consider chirplet transform subspaces,
leading to a variety of new transforms.
Thu Jan 8 19:50:27 EST 1998