Comparison of two eigenstructure algorithms for lossless multirate filter optimization

This paper compares the eigenstructure and modulation algorithms, which are used for two-channel lossless FIR lter optimization. We study the e ects of eigenvalue separation of the input covariance matrix and the step size on their convergence behavior. First, we show that the convergence rate of two algorithms increases as the separation of eigenvalues of the covariance matrix increases. The modulation algorithm (MA) converges more rapidly than the eigenstructure one (EA) because of its better eigenvalue separation. Second, the necessary condition for which the two algorithms converge is derived. Simulations are presented which support th analysis.