@ARTICLE{mannsp, author = "Steve Mann and Simon Haykin", title = "The Chirplet Transform: Physical Considerations", journal = "{IEEE} Trans. Signal Processing", year = "1995", volume = 43, number = 11, pages = 2745--2761", month = "November", organization = "The Institute for Electrical and Electronics Engineers"} # publisher = "{IEEE}", # in above line, IEEE doesn't get included so i put it as part of the journal

**Corresponding author: Steve Mann, currently with University
of Toronto, Department of Electrical Engineering, Computer Group,
10 King's College Road, Sandford Fleming Building, Room 2001, (416)946-3387,
mann@eecg.toronto.edu**

We consider a multidimensional parameter space formed by inner products
of a parameterizable family of *chirp* functions with a signal
under analysis.
We propose the use of quadratic chirp functions (which we will call
__q__-chirps for short),
giving rise to a parameter space that
includes both
the time-frequency plane and
the time-scale plane as two-dimensional subspaces.
The parameter space contains a ``time-frequency-scale volume'',
and thus encompasses both the short-time Fourier transform (as a
slice along the time and frequency axes), and the wavelet transform (as
a slice along the time and scale axes).

In addition to time, frequency, and scale, there are two other coordinate axes within this transform space: shear-in-time (obtained through convolution with a q-chirp) and shear-in-frequency (obtained through multiplication by a q-chirp). Signals in this multidimensional space can be obtained by a new transform which we call the ``q-chirplet transform'', or simply the ``chirplet transform''.

The proposed chirplets are generalizations of wavelets, related to each other by two-dimensional affine coordinate transformations (translations, dilations, rotations, and shears) in the time-frequency plane, as opposed to wavelets which are related to each other by one-dimensional affine coordinate transformations (translations and dilations) in the time-domain only.

- INTRODUCTION
- THE CHIRPLET
- CHIRPLET TRANSFORM SUBSPACES
- CONCLUSION
- References
- About this document ...

Thu Jan 8 19:50:27 EST 1998