A matrix filter is a linear and time-invariant operator on the space of vector-valued signals. Matrix filter bank is the generalization of filter bank. A perfect reconstruction matrix filter bank consists of an analysis matrix filter bank and a synthesis matrix filter bank. In the theory of filter design, generating a perfect reconstruction matrix filter bank from a given lowpass matrix filter is considered. Such a lowpass matrix filter is called a primary matrix filter. In this paper, we give a necessary and sufficient condition for a lowpass matrix filter being primary and discuss the relation between perfect reconstruction matrix filter bank and biorthogonal multiwavelet.
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