From this course, we hope that students gain an intuitive feel for basic discrete-time signal processing concepts, as well as an appreciation of the applications in which those concepts have been used. To this end, we are not placing the emphasis on the mathematical foundations of the course material, but instead on the reinforcement of qualitative concepts by hands-on laboratory work. When we introduce mathematical concepts, we appeal to the student's observation and intuition of physical phenomena.
After giving examples of sampled data in their daily lives, we introduce sampled signals by way of computer music [7]. We begin by discussing sinusoidal models for pure tones. By playing tones, the students hear the effect of changing magnitude, frequency, and phase on individual tones and on a sum of tones. In the next lecture, we present sampling and aliasing. We play properly sampled and aliased versions of the same speech and music signals to demonstrate how the harmful effects of aliasing are heard. In the corresponding laboratory, the students play a variety of tones to determine the frequency range of their own hearing, and undersample tones to hear aliasing.
For the next lecture, we introduce the concept of linear and non-linear systems, and the special case of linear time-invariant systems. We then play tones that have been processed by linear time-invariant, linear time-varying, and non-linear systems. The students can hear that the linear time-invariant system alters the amplitude but not the frequency of the tone. Since the ear is relatively insensitive to phase, the students are not able to distinguish the phase change in the single tone induced by the linear time-invariant system. For the linear time-varying system, we amplitude modulate the tone so the students hear the two resulting frequencies. We frequency modulate the tone to produce a rich set of tones for the example of a non-linear system. In the laboratory, the students experiment with representations of computer music. They play sequential tones to synthesize a bar of their favorite song, play multiple tones simultaneously, and modulate one tone with another. Time permitting, they can experiment with FM synthesis of musical tones.
Next, we introduce filtering from a qualitative point-of-view. We characterize filtering by passing certain qualities and rejecting others. We demonstrate the concept of lowpass and highpass filters by using tones and sampled waveforms. In the laboratory, the students code simple filters in MATLAB to produce a variety of simple digital audio effects, including vibrato, echo, reverberation, tremelo, and chorusing.