ABSTRACT
Much of thematerial we learn and teach in our DSP classes deal with
linear time invariant (LTI) systems. Linearity and time invariance
are important properties that led 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 newways of analyzing and synthesizing
LTV systems. We must give our students new approaches and tools
to test and probe implementations to verify proper operation aswell
as to debug and repair faulty realizations of multirate systems.
