Performance characteristics of critically decimated multirate adaptive systems

Multirate adaptive systems are known to require a nondiagonal form when critical decimation is used. This has been shown previously using quasi-perfect reconstruction filter banks and approximations of the inverse of the aliasing component matrix, H(z). The authors show the exact form of the adaptive solution by constraining the analysis and synthesis filter banks such that the analysis/synthesis system is a perfect reconstruction system, and the aliasing component matrix is unitary on the unit circle. They then demonstrate the performance of such a system, for the two-band and M-band case, using a tridiagonal approximation, in terms of subband eigenvalue disparity, convergence rate, computational complexity, and misadjustment. They show the importance of high stopband attenuation in the design of analysis filters for the M>2 channel case