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

A technology of wavelet transform and judgment method, applied in the field of signal processing, can solve problems such as huge amount of calculation

Inactive Publication Date: 2018-09-14
XI AN JIAOTONG UNIV
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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 u...

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

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Embodiment Construction

[0048] The content of the present invention will be further described below in conjunction with the accompanying drawings and tables.

[0049] In the mother wavelet function ψ(t), the discretization parameter a of the scaling factor 0 and the discretization parameter b of the time translation factor 0 In a given situation, the invention is a method for accurately estimating the upper and lower bounds of the discrete wavelet transform family and determining the frame. The present invention simultaneously estimates the upper bound and the lower bound of the discrete wavelet transform family by utilizing the existing technology and the developed new technology respectively, and comprehensively compares the estimation results of the two methods on this basis to obtain a smaller upper bound of the discrete wavelet transform family And a larger lower bound, and then achieve the purpose of judging whether the discrete wavelet transform family can constitute a wavelet frame and wheth...

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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...

Claims

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Application Information

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IPC IPC(8): G06F17/14
CPCG06F17/148
Inventor 王晓凯陈文超师振盛
Owner XI AN JIAOTONG UNIV
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