A Fast Computational Method for Simultaneous Compression Transformation and Reconstruction

Abstract

The invention discloses a fast calculation method for synchronous compression transformation and reconstruction, and the method comprises the steps: 1) selecting the standard deviation sigma of a Gaussian window, and calculating the length L of the window; 2) selecting a window function jumping point H; 3) performing overlapping segmentation on the original signal x [n], wherein the number of overlapping points is L-H, constructing a matrix X by taking each section of data as each column of the matrix; 4) multiplying the invariable discrete sequence g [n] corresponding to the window function by each column of the matrix X, and then performing FFT of Nf points on each column to obtain Sx [m, k]; 5) according to the selected frequency band, intercepting a sub-matrix for the Sx [m, k], and only rearranging along the frequency to obtain a time-frequency matrix Tx [m, l] after synchronous compression transformation; 6) performing inverse discrete Fourier transform on each column of Tx [m, 1] to obtain a double-variable function r [m, 1], and then multiplying the mth sequence r [m, 1] by a sliding window g [n-mH]; and adding the results to obtain a reconstructed signal. According to themethod, the operation efficiency is greatly improved while the excellent time-frequency aggregation of the synchronous compression transformation is ensured, and the reconstruction of the synchronouscompression inverse transformation can still be realized under a fast algorithm.

Description

technical field [0001] The invention belongs to the field of time-frequency analysis of non-stationary signals, in particular to a fast calculation method for synchronous compression transformation and reconstruction. Background technique [0002] The time-frequency analysis method is a signal analysis method for non-stationary conditions. It is different from the traditional signal analysis method that only considers the time domain or frequency domain. It transforms the one-dimensional time-domain signal into a two-dimensional joint time -Frequency domain (time-frequency domain) distribution function, which comprehensively considers the two variables of time and frequency, and can reveal the variation law of each component in the signal with time. From the perspective of transformation, time-frequency analysis methods can be roughly divided into two categories: linear time-frequency analysis methods and quadratic time-frequency analysis methods. Among them, linear time-fr...

AI Technical Summary

Problems solved by technology

[0004] Although the synchronous compressive transform has been widely concerned in time-frequency analysis algorithms and applications due to its excellent time-frequency aggregation and reconstruction characteristics, when using the synchronous compressive transform to analyze non-stationary signals in engineering practice, sometimes the number of data points is too large. In large cases, if the analysis algorithm is not handled properly, it will cause huge computational overhead

Images