‘Chirplets’ and ‘warblets’: novel time–frequency methods

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Abstract
A novel transform is proposed, which is an expanison of an arbitrary function onto a localised basis of multiscale chirps (swept frequency wave packets) for which the term ‘chirplets’ has been used. The wavelet transform is an expansion onto a basis of functions which are affine in the physical domain (e.g. time). In other words they are translates and dilates of one mother wavelet. The proposed basis is an extension of affinity, from the physical (time) domain, to the time-frequency domain. The basis includes both the wavelet and the short-time Fourier transform (STFT) as special cases (the degree of freedom modulation is simply attained through a translation in frequency). Furthermore, the basis include shear in time, and shear in frequency, leading to a broader class of chirping bases. Numerous practical applications of the chirplet have been found, such as in Doppler radar signal processing.

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