Polyphase matrices provide a compact, low-sample-rate description of multirate filter banks. By grouping samples into blocks (phases) and arranging the polyphase components of each analysis/synthesis filter into matrix polynomials in \(z^{-1}\) , filtering and (de)sampling reduce to simple matrix multiplications. This chapter builds the N-channel analysis and synthesis polyphase matrices, states the perfect reconstruction (PR) condition, and highlights the paraunitary case for guaranteed PR, paving the way for efficient, scalable filter bank designs (Vaidyanathan (1993) Multirate systems and filter banks. Prentice-Hall, Inc; Strang and Nguyen (1996) Wavelets and filter banks. Wellesley-Cambridge Press).