This chapter extends the transform-as-filter-bank view to the discrete cosine transform (DCT), with emphasis on the DCT-IV used widely in audio coding. We extract the equivalent analysis/synthesis impulse responses from the DCT-IV matrix and discuss their limited frequency selectivity (rectangular time support). To overcome these limits while retaining critical sampling and perfect reconstruction (PR), we introduce the polyphase representation. By reorganizing filtering and sampling into vector–polynomial products, polyphase turns “filter+decimate” into a low-rate matrix product in the z-domain and yields concise PR conditions.