# Overview of the Course

Signals convey information. Systems transform signals. This course introduces the mathematical models used to design and understand both. It is intended for students interested in developing a deep understanding of how to digitally create and manipulate signals to measure and control the physical world and to enhance human experience and communication.

Signals are defined as functions on respective sets. Examples include:

- Continuous-time signals (audio, radio, voltages);
- Discrete-time signals (digital audio, synchronous circuits);
- Images (discrete and continuous);
- Discrete-event signals; and
- Sequences.

Systems are defined as mappings on signals. The notion of the
*state* is discussed in a general way. Feedback systems and
automata illustrate alternative approaches to modeling *state* in
systems.
Frequency domain models for signals and frequency response for
linear time-invariant systems are investigated.
Sampling of continuous signals is discussed to relate continuous time
and discrete time signals.

Applications that are discussed include communications systems, audio, video, image processing systems, and control systems.

Although the course may be taken after Math 1b, certain topics from Math 54 (matrices and vectors) and CS 70 (discrete mathematics) can be quite helpful.

## Prerequisites

There is only one formal prerequisite:

- Math 1b, Calculus

In the Spring of 2000, we found that having one of Math 53, 54, or 55 (or CS 70) prior to or concurrent with this course had a significant impact on performance. Math 54 had a slightly greater impact than the others (see the statistical study for details).

## Papers

Two papers describing this course and the first version of its lab are available:

- Edward A. Lee and Pravin Varaiya,
"Introducing Signals
and Systems -- The Berkeley Approach,''
*Proc. of the First Signal Processing Education Workshop*, Hunt, Texas, October 15 - 18, 2000. - Edward A. Lee, "
Designing a Relevant Lab for Introductory
Signals and Systems,''
*Proc. of the First Signal Processing Education Workshop*, Hunt, Texas, October 15 - 18, 2000.