What is polyphase filter structure and why is it efficient?

Polyphase decomposition splits a filter into multiple subfilters (phases) that operate at reduced rate. For M-fold interpolation: H(z) = sum(z^(-k) * E_k(z^M)), each E_k processes at output rate, combined with upsamplers. Efficiency: Avoids computing outputs that will be discarded (decimation) or processing zero-valued samples (interpolation). Reduces computation by factor M. Used in: Efficient multirate systems, filter banks, channelizers, and sample rate converters. Implementation: Commutator structure switches between phase filters. Critical for practical multirate signal processing.