Frame analysis for biorthogonal cosine-modulated filterbanks

This paper addresses the efficient computation of frame bounds for cosine-modulated filterbanks. We derive explicit expressions for the eigenvalues of the frame operator that can be easily computed from the prototype's polyphase components. The number of channels and the downsampling factor may be even or odd, and the oversampling factor is supposed to be an integer. The analysis of low-delay, biorthogonal filterbanks; shows that prototypes solely designed to minimize the stopband energy may lead to wide open frames and, thus, to an undesirable numerical behavior. Because the computational cost of determining the frame bounds with the proposed method is very low, we can directly use the bounds during prototype optimization and obtain prototypes with minimum stopband energy under the condition of fixed frame bounds. Various design examples are presented. Disciplines Physical Sciences and Mathematics Publication Details This article was published as: Mertins, A, Frame analysis for biorthogonal cosine-modulated filterbanks, IEEE Transactions on Signal Processing, January 2003, 51(1), 172-181. Copyright IEEE 2003. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/92 172 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 51, NO. 1, JANUARY 2003 Frame Analysis for Biorthogonal Cosine-Modulated Filterbanks Alfred Mertins, Member, IEEE Abstract—This paper addresses the efficient computation of frame bounds for cosine-modulated filterbanks. We derive explicit expressions for the eigenvalues of the frame operator that can be easily computed from the prototype’s polyphase components. The number of channels and the downsampling factor may be even or odd, and the oversampling factor is supposed to be an integer. The analysis of low-delay, biorthogonal filterbanks shows that prototypes solely designed to minimize the stopband energy may lead to wide open frames and, thus, to an undesirable numerical behavior. Because the computational cost of determining the frame bounds with the proposed method is very low, we can directly use the bounds during prototype optimization and obtain prototypes with minimum stopband energy under the condition of fixed frame bounds. Various design examples are presented.This paper addresses the efficient computation of frame bounds for cosine-modulated filterbanks. We derive explicit expressions for the eigenvalues of the frame operator that can be easily computed from the prototype’s polyphase components. The number of channels and the downsampling factor may be even or odd, and the oversampling factor is supposed to be an integer. The analysis of low-delay, biorthogonal filterbanks shows that prototypes solely designed to minimize the stopband energy may lead to wide open frames and, thus, to an undesirable numerical behavior. Because the computational cost of determining the frame bounds with the proposed method is very low, we can directly use the bounds during prototype optimization and obtain prototypes with minimum stopband energy under the condition of fixed frame bounds. Various design examples are presented.