MULTIRATE FILTER BANKS WITH BLOCK SAMPLING

Multirate filter banks with block sampling were recently studied by Kh ansari and Leon-Garcia. In this paper, we want to systematically study multirate filter banks with block sampling by studying general vector filter banks where the input signals and transfer functions in conven tional multirate filter banks are replaced by vector signals and trans fer matrices, respectively, We show that multirate filter banks with b lock sampling studied by Khansari and Leon-Garcia are special vector f ilter banks where the transfer matrices are pseudocirculant, We presen t some fundamental properties for the basic building blocks, such as N oble identities, interchangeability of down/up sampling, polyphase rep resentations of M-channel vector filter banks, and multirate filter ba nks with block sampling, We then present necessary and sufficient cond itions for the alias-free property, finite impulse response (FIR) syst ems with FIR inverses, paraunitariness, and lattice structures for par aunitary vector filter banks. We also present a necessary and sufficie nt condition for paraunitary multirate filter banks with block samplin g, As an application of this theory, we present all possible perfect r econstruction delay chain systems with block sampling, We also show so me examples that are not paraunitary for conventional multirate filter banks but are paraunitary for multirate filter banks with proper bloc k sampling, In this paper, we also present a connection between vector filter banks and vector transforms studied by Li, Vector filter banks also play important roles in multiwavelet transforms and vector subba nd coding.