Vector filter banks and multirate filter banks with block sampling

We study general vector filter banks where the input signals and transfer functions in conventional multirate filter banks are replaced by vector signals and transfer matrices, respectively. We show that multirate filter banks with block sampling and linear time invariant transfer functions studied by Khansari and Leon-Garcia (see IEEE Trans. on Signal Processing, vol.41, p.3365-3376, Dec. 1993) are special vector filter banks where the transfer matrices are pseudo-circulant. We then present necessary and sufficient conditions for the alias free property, FIR systems with FIR inverses, paraunitariness for vector filter banks. We also present a necessary and sufficient condition for paraunitary multirate filter banks with block sampling