Design of signed powers-of-two coefficient perfect reconstruction QMF bank using CORDIC algorithms

Lattice structures have several advantages over the tapped delay line form, especially for the hardware implementation of general digital filters. It is also efficient for the implementation of quadrature mirror filter (QMF), because the perfect reconstruction is preserved under the coefficient quantization. Moreover, if lattice coefficients are implemented in signed powers-of-two (SPT), the hardware complexity can also be reduced. But the discrete coefficient space with the SPT representation is sparse when the number of nonzero bits is small. This paper proposes a structure of orthogonal QMF lattice with SPT coefficients, which has much denser discrete coefficient space than the conventional structure. While the conventional approaches directly quantize the lattice coefficients into SPT form, the proposed algorithm considers the quantization in the SPT angle space. For this, each lattice stage is implemented by the cascade of several variants of COordinate Rotation Digital Computer. The resulting angle space and corresponding discrete coefficient space is much denser than the one generated by the conventional direct quantization approach. An efficient coefficient search algorithm for this structure is also proposed. Since the proposed architecture provides denser coefficient space, it shows less coefficient quantization error than the conventional QMF lattice. Index Terms--COordinate Rotation Digital Computer (CORDIC), lattice filter, perfect reconstruction (PR), quadrature mirror filter (QMF), signed powers-of-two (SPT).