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
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.
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).
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.