A sequential reoptimization approach for the design of signed power-of-two coefficient lattice QMF bank

This paper presents a sequential optimization approach for the design of lattice structure quadrature mirror filter (QMF) banks subject to the sum of signed power-of-two (SPT) coefficient constraints. The lattice structure QMF bank structurally guarantees the perfect reconstruction (PR) property. Nevertheless, its frequency response is still adversely affected by coefficient quantization. In this paper, a frequency response deterioration measure is developed from the lattice coefficient analysis. Based on this frequency response deterioration measure, the coefficient which will cause the largest deterioration in the frequency response of the filter is selected for quantization first. After the coefficient is quantized, the remaining unquantized coefficients are reoptimized. The process of quantizing the coefficient and reoptimizing the remaining unquantized coefficient is repeated until all the coefficients are quantized. The frequency responses of the filters obtained using our algorithm are significantly superior to those obtained by simple rounding of the coefficient values.