Matrix decomposition structure of two-channel quadrature mirror filter bank and coefficient design method thereof

A matrix decomposition structure of a two-channel quadrature mirror filter bank, comprising an analysis filter part, a synthesis filter part and a connecting part, wherein the analysis filter part and the synthesis filter part have a same structure, and the analysis filter part comprises one E0,M module, D X modules, one Y module, D Z modules, a total input port Input, and total outputs Output0 and Output1;

• a dth X module Xd comprises p multipliers, 2·(p−1) adders and 2·(p−1) delayers, d=1, 2, . . . D;
• an input port of the multiplier is connected with the total input port Input;
• at a first time point, outputs of the p multipliers are delayed and added in a sequence from back to front to obtain an output Id,0;
• and at a next time point, the outputs of the p multipliers are delayed and added in a sequence from front to back to obtain an output Id,1;
• the Y module comprises D2 multipliers and D adders;
• a multiplier yd,1, a multiplier yd,2, . . . , a multiplier yd,D take the Id,0 as an input at the first time point, and take the Id,1 as an input at the next time point;
• and outputs of a multiplier y1,d, a multiplier y2,d . . . a multiplier yD,d pass through one adder to obtain an output Jd;
• structures of the Z module and the E0,M module are the same as that of the X module, and a dth Z module takes the output Jd of the Y module as the input of the multiplier;
• and the Input port of the multiplier in the E0,M module is connected with the total input port Input through the delayer, so that an output O0 is obtained at the first time point;
• and an output O1 is obtained at the next time point;
• and
• at the first time point, outputs of the D Z modules are added with the output O0 of the E0,M module, and output from the total output port Output0 of the analysis filter part, and the Output1 remains unchanged;
• and at the next time point, the outputs of the D Z modules are added with the output O1 of the E0,M module, and output from the total output port Output1 of the analysis filter part, and the Output0 remains unchanged.