Teaching Programming and Debugging Techniques for Multirate Signal Processing
fred harris, Chris Dick · 2018
Much of the material we teach in our DSP classes deal with linear time invariant (LTI) systems. Linearity and time invariance are important properties that lead to insight and comprehension through capable analysis and synthesis tools. We learn to appreciate the importance of impulse response, convolution, transfer functions, frequency response, and the Nyquist sampling criterion. When we introduce multirate signal processing we introduce the process of resampling and we find ourselves in unfamiliar territory. The quote “Toto, I've a feeling we're not in Kansas anymore!” comes to mind. Dorothy was right! We are now in the land of linear time varying (LTV) systems. In this land we embed one or more sample rate changes in the signal flow path which result in systems with multiple impulse responses. We become uncomfortably aware that the system does not have a transfer function and that our analysis and synthesis tools don't work here. We must develop new perspectives while teaching new ways of analyzing and synthesizing LTV systems. We must give our students new approaches and tools to test and probe implementations to verify proper operation as well as to debug and repair faulty realizations of multirate systems.