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

The lattice structure quadrature mirror filter (QMF) bank structurally guarantees the perfect reconstruction (PR) property. Thus, it is eminently suitable for hardware realization even under the severe coefficient quantization condition. Nevertheless, its frequency response is still adversely affected by coefficient quantization. In this paper, a novel technique is presented for the design of lattice structure PRQMF banks subject to discrete coefficient value constraints. In our technique, the coefficient values are quantized sequentially one at a time. After each coefficient is being quantized, the remaining unquantized coefficient values are reoptimized to partially compensate for the frequency response deviation caused by the quantization of that coefficient value. The order of selection of the coefficients for quantization is based on a coefficient sensitivity measure. Coefficients with higher sensitivity measures are quantized earlier than coefficients with lower sensitivity measures. The improvement in the frequency response ripple magnitude achieved by our algorithm over that by simple rounding of coefficient values differs widely from example to example ranging from a fraction of a dB to over 10 dB.