high-precision Gabor time-frequency analysis method based on a signal sparse representation theory

Abstract

The invention discloses a high-precision Gabor time-frequency analysis method based on a signal sparse representation theory. In order to solve the high-precision Gabor time-frequency spectrum coefficient, the method comprises the following steps of firstly, solving the optimal window width selection problem of discrete Gabor transform (DGT), calculating transform coefficient aggregation evaluation values corresponding to different window widths under the high aggregation constraint condition of the transform coefficient, and finding out the optimal window width; Secondly, solving a high-aggregation traditional DGT coefficient solving problem, converting the high-aggregation DGT coefficient solving problem into an optimization problem for solving a sparse solution of the high-aggregation DGT coefficient solving problem by utilizing a signal sparse representation theory according to an equivalent relation between aggregation of a transformation coefficient and sparsity of the transformation coefficient, and proposing a rapid solving algorithm of the optimization problem; The research of the invention enriches and perfects the Gabor time-frequency analysis theory, and has important theoretical significance and application value.

Description

technical field [0001] The invention belongs to signal and information processing technology, in particular to a high-precision Gabor time-frequency analysis method based on signal sparse representation theory. Background technique [0002] Fourier transform is the most commonly used method for analyzing and processing stationary signals, and it is widely used in communication and automatic control, signal and image processing, machine vision and other fields. However, since the Fourier transform changes the time function into a frequency function, the frequency function has no local time frequency information, so it cannot express the time-frequency locality of the signal, and the Fourier spectrum generated by the Fourier transform coefficients cannot express the signal How the frequency component changes with time, and the nature of the frequency component changing with time is precisely the most fundamental and critical property of non-stationary signals such as speech, r...

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Problems solved by technology

[0004] The original Gabor expansion is continuous in time, infinitely long and non-periodic. For a long time after it was proposed, although the Gabor expansion was recognized as useful, it was difficult to calculate its expansion or transformation coefficients. has been restricted

The main reason for the difficulty in calculating Gabor expansion or transformation coefficients is that the basis functions of Gabor expansion are not orthogonal, and the usual inner product rule cannot be used to calculate expansion coefficients

In addition, the Gabor expansion and transformation are complex-valued forms, which are generated by introducing a series of basis functions capable of time-shifting and frequency-shifting on the basis of the complex-valued Fourier transform. The basis function values ​​and transformation coefficients are complex numbers, and the period The research on the real-valued discrete Gabor expansion and transformation of is almost blank

[0005] In the in-depth study of the Gabor time-frequency analysis method, we found that the Gabor time-frequency spectrum generated by the discrete Gabor transform coefficients, even if a large number of time-frequency sampling points is taken, its time-frequency resolution accuracy is not high, and it is extremely susceptible to The root cause of this problem is the influence of the window width of the window function, firstly because the transformation coefficients obtained by the traditional discrete Gabor transform are not highly aggregated, and secondly because the window function is restricted by the Heisenberg uncertainty principle, that is, Its time width and bandwidth cannot be infinitely small at the same time, and the product of the two is greater than or equal to a constant value (0.25 / π); that is to say, the time width and bandwidth of the window function are contradictory and inversely proportional

This has a great impact on the aggregation of the discrete Gabor transform coefficients. The Gabor time spectrum corresponding to the window function with a small time width has better time resolution accuracy but poor frequency resolution accuracy because the window function has a larger bandwidth. ; Conversely, the Gabor time spectrum corresponding to the window function with a larger time width has poorer time resolution accuracy but better frequency resolution accuracy, because the window function has a smaller bandwidth

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