Model and Data-Driven Homework Problems for Learning Signal Processing Concepts

The Electrical and Computer Engineering Department at Portland State University offers a course in Sensor Array Processing. The content is designed to be introductory and approachable for undergraduate, first year graduate and students from other disciplines such as Mechanical Engineering or Physics. The signal processing techniques explored use two or more sensors and can be applied to acoustics or electromagnetic waves. I have two favorite homework problems: one is based on simulated data and the other based on measured data and both help solidify important concepts. For the simulations, a model is developed based on the method of images and can be applied to signals from a sonar in the ocean or to voices in a room. These multipath environments are used to illustrate how a signal (such as an audio clip the student creates) would change in different environments or source/receiver geometry. The channel impulse response is modeled and together with convolution allows different waveform responses to be easily computed. My favorite problem using measured data is based on recordings of a broadband source on two sensors. Cross-correlation is used to determine the source direction. This problem explores the concepts of pulse compression and pre-whitening for time-delay and direction estimation