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 wavelets (``chirplets'').
- 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) parameter space.
- We next consider non-Gaussian analysis functions, giving rise to a five-dimensional parameter space.
- 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
governed
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