Optimized design method of M channel over-sampling modulation graph filter group

[0100] Simulation example 1:

[0101] Design a graph filter bank with the following parameters:

[0102] L h0 =12,L h1 =12,L g0 =11,L g1 =11,λ pd0 =0.3,λ pd1 =0.35,λ pd2 =0.55,λ sd0 =0.55,λ sd1 =0.1,λ sd2 =1.0,α=0.1,ε r =10 -10; the resulting graph filter bank magnitude response is image 3 As shown, PR in the figure represents the reconstruction error of the graph filter bank corresponding to different λ values. The values ​​of the maximum reconstruction error and orthogonality obtained by the simulation calculation are E, respectively max =3.31×10 -10 , Θ=0.8883, under the same graph filter bank length and operating environment, table 1 provides the method of the present invention and existing method 1 (close to orthogonal M channel oversampling), existing method 3 (a design M A new method for channel bi-orthogonal oversampled graph filterbanks) reconstruction performance and boundary ratio comparison of graph filterbanks designed.

[0103] Table 1

[0104]

[0105] R B to the boundary ratio [14] , Take R when simulating B Compared with the maximum value of , R B Equal to 1 indicates that the filter bank is completely reconstructed, and the reconstruction characteristics of the filter bank are better at this time. The comparison shows that the reconstruction error of the algorithm in this paper is obviously lower than that of the existing method 1 and the existing method 3, and the spectral characteristics of the graph filter bank designed by the method of the present invention are obviously better than those of the existing method 1 and the existing method 3. Both the error and the spectral selectivity are important indicators to measure the performance of the graph filter bank. Therefore, the overall performance of the modulation graph filter bank designed by the method of the present invention is better.

[0106] Simulation example 2:

[0107] Design a graph filter bank with the following parameters:

[0108] L h0 =8,L h1 =8,L g0 =7,L g1 =7,λ pd0 =0.3,λ pd1 =0.35,λ pd2 =0.55,λ sd0 =0.55,λλ sd1 =0.1,λ sd2 =1,α=0.1,ε r =10 -13; the resulting modulation map filter bank amplitude response is Figure 4 shown. Under the same graph filter bank length and operating environment, table 2 provides the method of the present invention and existing method 2 (M channel oversampling graph filter bank), existing method 3 (a design M channel bi-orthogonal filter bank) Comparison of reconstruction performance and orthogonality of graph filterbanks designed by a new method for sampled graph filterbanks.

[0109] Table 2

[0110]

[0111] The closer the orthogonality Θ is to 1, the better the orthogonality of the filter bank. It can be seen from the comparison that the reconstruction error of the graph filter bank designed by the method of the present invention is obviously smaller than that of the existing method 2 and the existing method 3, and its orthogonality is better than that of the existing method 2, and is equivalent to the existing method 3. The overall spectral characteristics are better than the existing method 2 and the existing method 3, so the overall performance of the graph filter bank designed in this paper is better.