A successive reoptimization approach for the design of discrete coefficient perfect reconstruction lattice filter bank

A Novel Genetic Algorithm for the Design of a Signed Power-of-Two Coefficient Quadrature Mirror Filter Lattice Filter Bank

“…The result of our GA is also better than the result of 39.85 dB reported in [17] because the coefficient values in this paper are allocated with a different number of SPT terms while keeping the total number of SPT terms fixed, rather than allocating exactly the same number of SPT terms to each coefficient as in [17]. Some filter banks denoted as 32E, 24D in [32] were designed in [8], [26] and the SPT coefficients were also reported.…”

“…The specifications are the same as those reported in [17], i.e., the lowpass filter's stopband edge is at 0.64π and its stopband frequency response is required to be equiripple; each coefficient value is represented as a sum of SPT terms; the smallest power-of-two term is 2 −12 . The only difference is that, in our example, the average number of SPT terms of each coefficient is 2, rather than having exactly 2 SPT terms allocated to each coefficient as in [17]. The population pool size and the mating pool size are 1000 and 100, respectively.…”

“…Quadrature mirror filter (QMF) banks [1], [5], [8], [17], [18], [20], [25], [26], [31], [32], have been used in various signal processing applications including subband coding of speech and image signals. A lattice analysis/synthesis system, which structurally ensures perfect reconstruction (PR), was introduced in [32].…”

“…For example, [8] reported a method involving a search in the discrete space in the vicinity of an optimum continuous coefficient space. A successive reoptimization approach was introduced in [17].…”

Filter Design With Low Complexity Coefficients

“…Coefficient truncation subsequently appeared in other fields like speech processing [5] and control [6]. Several methods have been proposed for coefficient truncation: exhaustive search over possible truncated coefficients [3], successive truncation of coefficients and reoptimization over remaining ones [4], [7], local bivariate search around the scaled and truncated coefficients [8], tree-traversal techniques for truncated coefficients organized in a tree according to their complexity [9], [10], coefficient quantization using information-theoretic bounds [11], weighted least-squares [12], simulated annealing [13], [14], genetic algorithms [15]- [17], Tabu search [18], design of optimal filter realizations that minimize coefficient complexity [13]. Other approaches have formulated the problem as a nonlinear discrete optimization problem [19], or have used integer programming techniques [20]- [22].…”