Overview

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.