## ENEE322 Signals and Systems Theory

*Course Description*: The course introduces continuous and discrete-time linear systems, their response to various signals, and the mathematical tools needed to represent the system response in the time and frequency domains. The mathematical techniques studied in the course rely on Fourier analysis of discrete-time and continuous signals (Fourier series and Fourier integrals) as well as on related tools such as the continuous and discrete Laplace transforms. The course emphasizes basic properties of linear systems such as time-invariance, stability, invertibility, and causality and their links with the representation of the impulse response and transfer functions of the system. The mathematical concepts are illustrated by examples of mechanical, electrical, and other systems such as models for compounded interest and population growth.

Prerequisite(s): ENEE222; MATH246

Corequisite(s): None

Course Objectives:

- To understand harmonic analysis of periodic and aperiodic signals, their frequency composition and the importance of filters in system design
- To develop the ability to predict and analyze the response of linear systems to various types of input signals in both quantitative and qualitative terms
- To develop the ability to use transforms as the mathematical toolbox for the analysis of signals and systems, to be able to determine which of the transforms applies to the analysis of a given discrete-time or continuous-time system, and to be able to calculate direct and inverse transforms of simple signals

*Topics Covered*:

- Signals, their properties and representation. Periodic signals. Unit impulse and unit step signals
- Linear systems and their properties. Causality, stability, time-invariance, invertibility
- Representation of systems by block diagrams, differential or difference equations
- Fourier series representation of periodic signals. Energy and power signals, distribution of energy over the spectrum of the signal. Discrete-time Fourier series and their use for the harmonic analysis of discrete signals
- Development of the Fourier transform as a limiting case of Fourier series of periodic signals with increasing period. Continuous and discrete-time Fourier transforms
- The use of Fourier transforms for the analysis of linear systems represented by block diagrams and differential equations
- The continuous-time Laplace transform, its properties and its relation to the Fourier transform
- The use of the Laplace transform for the analysis of linear systems. Bode plots as a tool for the analysis of first- and second-order systems
- The z-transform and its use for the analysis of linear-time systems