Polyphase filters - A model for teaching the art of discovery in DSP

By its very nature DSP is a mathematically heavy topic and to fully understand it students need to understand the mathematical developments underlying DSP topics. However, relying solely on mathematical developments often clouds the true nature of the foundation of a result. It is likely that students who master the mathematics may still not truly grasp the key ideas of a topic. Furthermore, teaching DSP topics by merely "going through the mathematics" deprives students of learning the art of discovery that will make them good researchers. This paper uses the topic of polyphase decimation and interpolation to illustrate how it is possible to maintain rigor yet teach using less mathematical approaches that show students how researchers think when developing new ideas.