Structure and Interpretation of Signals and Systems

Structure and Interpretation of Signals and Systems
This course is an introduction to mathematical modeling techniques used in the design of electronic systems. An important keyword here is "mathematical."

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.

Automata theory is studied using Mealy machines with input and output. Notions of equivalence of automata and concurrent composition are introduced.

Hybrid systems combine time-based signals with event sequences.

Difference and differential equations are considered as models for linear, time-invariant state machines.

Frequency domain models for signals and frequency response for systems are investigated.

Sampling of continuous signals is discussed to relate continuous time and discrete time signals.

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