The Chirplet Transform: Physical Considerations

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 special cases. This 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 shearin -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 "chiplet transform". The proposed chirplets..