Upper and low limit accurate estimation and framework determination method for discretized wavelet transformation family

Abstract

The invention discloses an upper and low limit accurate estimation and framework determination method for a discretized wavelet transformation family. The method comprises the following steps: step 01: a user collects data while setting a discretized wavelet family; step 02: according to the set scale stretch factor discretization parameter a0, discretizing the frequency f within the range from 1to a0 in order to obtain a series of discretized frequency values f; step 03: using conventional method within the frequency domain to estimate in order to obtain an upper Aold and a lower Bold for the discretized wavelet transformation family; step 04: using a novel method within the frequency domain to estimate in order to obtain an upper limit Anew and a lower limit Bnew for the discretized wavelet transformation family; step 05: obtaining an upper limit A and a lower limit B for the discretized wavelet transformation family by integrating Aold, Bold, Anew and Bnew; step 06: determining whether the discretized wavelet transformation family can form a wavelet framework or not; and step 07: if so, utilizing the framework to carry out data processing. The upper and low limit accurate estimation and framework determination method can be used for determining whether the discretized wavelet transformation family can form the wavelet framework or not and whether the discretized wavelet transformation family can be used for data processing. Meanwhile, the method is featured by being simple in implementation, easy in operation and broad in application scope.

Description

technical field [0001] The invention belongs to the field of signal processing, in particular to a method for accurately estimating the upper and lower bounds of a discrete wavelet transform family and determining a frame. Background technique [0002] Continuous wavelet transform is a commonly used time-frequency decomposition method in the field of signal processing, which has the advantages of simple theory and easy implementation. The continuous wavelet transform cross-correlates the time-translated and scale-stretched wavelet function with the one-dimensional continuous signal to obtain the continuous wavelet transform coefficients, which can analyze the one-dimensional continuous signal more clearly and intuitively from the time-scale domain. If the time-domain form of the mother wavelet is ψ(t) (its frequency-domain form is Ψ(f)), the wavelet after scale a stretching and time b translation is (its frequency domain form is Then the continuous wavelet transform coef...

AI Technical Summary

Problems solved by technology

[0012] Disadvantages: 1. This technique estimates the upper and lower bounds, not the upper and lower bounds, and when a 0 and b 0 When is large, the estimated upper bound is larger and the lower bound is smaller

[0013] 2. The range of summation is from negative infinity to positive infinity, and the amount of calculation is huge

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