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@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 = 27452761", 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)9463387, 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 qchirps for short), giving rise to a parameter space that includes both the timefrequency plane and the timescale plane as twodimensional subspaces. The parameter space contains a ``timefrequencyscale volume'', and thus encompasses both the shorttime 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: shearintime (obtained through convolution with a qchirp) and shearinfrequency (obtained through multiplication by a qchirp). Signals in this multidimensional space can be obtained by a new transform which we call the ``qchirplet transform'', or simply the ``chirplet transform''.
The proposed chirplets are generalizations of wavelets, related to each other by twodimensional affine coordinate transformations (translations, dilations, rotations, and shears) in the timefrequency plane, as opposed to wavelets which are related to each other by onedimensional affine coordinate transformations (translations and dilations) in the timedomain only.