基于余弦滚降特性的IIR余弦调制滤波器组的设计

提出一种新的近似完全重构因果稳定的IIR余弦调制滤波器组的设计方法.基于所定义的一种IIR余弦滚降原型滤波器,滤波器组所要求的平坦条件完全被满足.在预先给定极点值的条件下,滤波器组的设计问题可以写成一个凸极大极小优化问题,从而采用二阶锥规划法求解.求出的滤波器组具有合理的完全重构误差,且原型滤波器的多相因子的分母相同,简化了完全重构条件.采用该滤波器组作为约束非线性优化法的有效初值,进一步优化得到完全重构IIR余弦滤波器组.

Design of IIR cosine modulated filter banks with approximate cosine-rolloff transition band

An efficient method was proposed for designing nearly perfect reconstruction (NPR)cosine modulated filter banks (CMFBs) with IIR prototype filters having an approximate cosinerolloff (CR) transition band. The polyphase components of the prototype filters of these IIR CMFBs had the same denominator so as to simplify the PR condition. By using a prototype filter with a CR transition band, the flatness condition required for an NPR CMFB was automatically satisfied. Based on some given poles values, the design problem was formulated as a convex minimax optimization problem and solved by second order cone programming (SOCP). The NPR IIR CMFB so obtained had a reasonably low reconstruction error and it was employed as the initial guess to constrained nonlinear optimization software for designing the PR IIR CMFB.Design results show that both NPR and PR IIR CMFBs with good frequency characteristics can be obtained by the proposed method.