Time-Domain Matrix Analysis of Polyphase FIR Filters

Polyphase filter design is a common subject studied in discrete systems analysis and digital signal processing (DSP) courses. However, the classic z-domain analysis, utilizing the noble identities, gives a conclusion to the true physical structures of polyphase filters which may not be obvious to many students. The proposed time-domain analysis provides a more straightforward development of polyphase implementation of interpolation and decimation functions, and hopes to provide students with a more visual representation of the polyphase interpolation and decimation processes. Results from a student survey show that over 73% of students believe that the proposed polyphase analysis strengthened their understanding of polyphase filters, and over 71% would prefer to use the proposed method over the traditional z-domain analysis when explaining polyphase filters to others.