Method of Chirp time-frequency atoms denoted with three parameters

Abstract

The invention discloses a simplified representation method of Chirp time-frequency atoms in self-adaption signal decomposition. For representation of time-frequency characteristics of non-stationary signals, time-frequency atoms of a better local time-frequency structure are used for replacing orthogonal basis functions, and linear combination of the best time-frequency atoms is used for representing signals. The time-frequency atoms are obtained through calculation by applying various operators on basic functions, the more operators applied on the basic functions, the more parameters the time-frequency atoms obtain, the stronger local capacity of the time-frequency atoms matching or approaching signals, while the harder the finding of optimal time-frequency atoms. The Chirp time-frequency atoms can well match frequency linear variation elements in the signals and approach nonlinear frequency variation elements. The Chirp time-frequency atoms are commonly represented by 4 parameters of proportion, time shift, frequency shift and linear frequency modulation. The simplified representation method of the Chirp time-frequency atoms in the self-adaption signal decomposition introduces revolve-radial shift operators and composition operators through fractional order Fourier transform to obtain the Chirp time-frequency atoms represented by the three parameters of proportion, revolve and radial shift. According to the simplified representation method of the Chirp time-frequency atoms in the self-adaption signal decomposition, advantages of more concise representation, more definite physical significance of each parameter, great time reduction for searching the optimal time-frequency atoms can be obtained.

Description

technical field [0001] The invention relates to a simplified representation method of Chirp time-frequency atoms in adaptive signal decomposition. Chirp time-frequency atoms are generally represented by four parameters: scale, time shift, frequency shift, and chirp. The present invention introduces rotation operator and radial shift operator through fractional Fourier transform, and can obtain Chirp time-frequency atom represented by three parameters of scale, rotation and radial shift. Background technique [0002] In order to describe the local time-frequency characteristics of non-stationary signals, in adaptive signal decomposition, time-frequency atoms with better local time-frequency structure are often used to replace the basis functions of orthogonal decomposition, and the best linear combination of time-frequency atoms is used to describe non-stationary signals. The time-frequency atom is obtained by performing various operator operations on the basic functions. T...

AI Technical Summary

Problems solved by technology

Gabor atoms can represent many non-stationary signals, but because their frequency is constant, the matching degree with the Chirp component whose frequency changes with time in the signal is low, and multiple Gabor time-frequency atoms can be used to represent a Chirp component, that is, a complete Chirp components are decomposed and diffused to multiple Gabor time-frequency atoms, which is not conducive to signal feature extraction and signal sparse representation

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