An instantaneous frequency identification method of vibration signal based on linear chirplet transform and Wigner-Ville distribution is presented. This method has an obvious advantage in identifying closely spaced and time-varying frequencies. The matching pursuit algorithm is employed to select optimal chirplets, and a modified version of chirplet transform is presented to estimate nonlinear varying frequencies. Because of the high time resolution, the modified chirplet transform is superior to the original method. The proposed method is applied to time-varying systems with both linear and nonlinear varying stiffness and systems with closely spaced modes.
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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 2-D 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 2-D affine coordinate transformations translations, dilations, rotations, and shears in the time-frequency plane, as opposed to wavelets, which are related to each other by 1-D affine coordinate transformations translations and dilations in the time domain only. Article :. Date of Publication: Nov DOI: Need Help?
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On a Chirplet Transform Based Method for Co-channel Voice Separation
Updated 29 Jul The Original Chirplet Transform Algorithm is introduced in ; while the codes here is motivated by , which provides a new insight to the Chirplet Transform. Peng Z. K , Meng G.
P-Chirps and P-Chirplets
In signal processing , the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets. Similar to the wavelet transform , chirplets are usually generated from or can be expressed as being from a single mother chirplet analogous to the so-called mother wavelet of wavelet theory. The term chirplet transform was coined by Steve Mann , as the title of the first published paper on chirplets. The term chirplet itself apart from chirplet transform was also used by Steve Mann , Domingo Mihovilovic, and Ronald Bracewell to describe a windowed portion of a chirp function. In Mann's words:. A wavelet is a piece of a wave, and a chirplet, similarly, is a piece of a chirp.