Optimal Design Method of Graph Filter Bank Based on Two-step Method
A filter bank and optimization design technology, applied in the field of signal processing, can solve problems such as the inability to take into account the frequency characteristics of the prototype filter
Active Publication Date: 2017-04-12
GUILIN UNIV OF ELECTRONIC TECH
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Problems solved by technology
[0004] The technical problem to be solved by the present invention is that the existing two-channel biorthogonal graph filter bank cannot take into account the frequency characteristics of the prototype filter, and a two-step method based on the optimal design method of the graph filter bank is provided
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[0027] A graph filter bank optimization design method based on a two-step method is characterized in that it comprises the following steps:
[0028] The first step: the structure of the graph filter bank is as follows figure 1 shown. Express each prototype filter of a graph filter bank as a polynomial function with respect to the characteristic roots:
[0029]
[0030]
[0031] Step 2: Transform the passband flatness of the prototype filter into the coefficient h of the prototype filter 0 , g 0 The function:
[0032]
[0033]
[0034] Step 3: Transform the stopband energy of the prototype filter into the coefficient h of the prototype filter 0 , g 0 The function:
[0035]
[0036]
[0037] Step 4: Express the full reconstruction condition of the graph filter bank as:
[0038]
[0039] Step 5: The design problem of the graph filter bank is reduced to the following optimization problem:
[0040]
[0041] In the formula, E p (h 0 ) represents the...
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The invention discloses a method for optimally designing graph filter banks on the basis of a two-step process. The method includes converting requirements on reconstruction characteristics and frequency characteristics of the filter banks into functions related to coefficients of prototype filters; converting design problems of the graph filter banks into a constrained optimization problem according to design requirements; ultimately solving the optimal coefficients of the prototype filters by the aid of the two-step process. The method has the advantages that optimization ideas are introduced into designs of the graph filter banks for the first time, and the reconstruction characteristics and the frequency characteristics of the graph filter banks are taken into consideration by the aid of factor regulating modes; the reconstruction characteristics and the frequency characteristics of the filter banks can be taken into consideration by optimization paths as compared with existing methods on the basis of polynomial decomposition; compromising effects can be realized between the reconstruction characteristics and the frequency characteristics by means of regulating parameters epsilon r under the condition of given lengths of graph filters.
Description
technical field [0001] The invention belongs to the field of signal processing, and in particular relates to a graph filter bank optimization design method based on a two-step method. Background technique [0002] In recent years, the processing of network big data has attracted widespread attention. These data are often defined on irregular geometric structures, such as social networks, wireless sensor networks, and financial networks. Traditional models based on rule-based location definitions cannot be used in the processing of such data. Graph (graph) is considered to be an effective model for describing such data. The nodes of the graph represent the location of the data, the size of the data can be represented by the graph node signal, and the connection between the nodes in the graph can represent different data. Relationships between nodes. On this basis, graph-based data signal processing becomes the key. In many applications, the amount of data is very large, an...
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IPC IPC(8): H03H21/00
Inventor 蒋俊正周芳程小磊欧阳缮刘庆华谢跃雷江庆郭云穆亚起
Owner GUILIN UNIV OF ELECTRONIC TECH