# ELEC 323

## Summary:

This course examines continuous-time signals and their properties, and briefly considers basic discrete-time and digital signals. Basic properties of systems with and without memory are discussed, as well as the concept of state, initial conditions, zero-input and zero-state responses. Discrete- and, in greater emphasis, continuous-time linear, time-invariant (LTI) systems are examined, including discrete and continuous-time convolutions, convolution integral and calculation, and LTI systems and differential equations. Students will learn about continuous-time signal analysis, such as the Fourier series and transform, Fourier Transform Analysis including filtering and frequency response, and the Laplace transform. This course builds on and supplements knowledge from other courses, including ELEC 221, MATH 235 and 236.

## Objectives:

By the end of the course students will be able to:

• Analyse systems and determine whether they are linear, time-invariant, causal, dynamic, and stable.
• Determine the unit impulse response of an LTI system and use it to calculate the system output produced by a given input.
• Find the Fourier series of periodic signals.
• Carry out Fourier transform analysis, including filtering, and determine the frequency response.
• Use the Laplace transform to analyse continuous-time systems, including RLC circuits.
 Work Assigned: There are several bi-weekly problem assignments and three MATLAB labs. Evaluation: Assignments 7% Each of 3 Labs (including Quiz or Report) 6% Midterm Exam 25% Final Exam 50% Resources: Textbook: M.J. Roberts, Signals and Systems, McGraw Hill, 2004.

## Outline:

Week 1: 1) Introduction to signals; 2) continuous-time signals and their properties; 3) basic discrete-time and digital signals

Week 2: 1) Introduction to systems; 2) systems with and without memory, concept of state, initial conditions, zero-input and zero-state responses; 3) basic properties of systems

Week 3: 1) Basic system description; 2) discrete- and continuous-time linear, time-invariant (LTI) systems, discrete and continuous-time convolutions; 3) convolution integral and calculation, LTI systems and differential equations

Week 4: 1) Continuous-time signal analysis; 2) Fourier series and transform; 3) types of signals, orthogonality of complex exponentials

Week 5: 1) Fourier series of periodic signals; 2) Fourier transform; 3) relation between Laplace and Fourier transforms

Week 6: 1) Properties of Fourier transform; 2) convolution; 3) Fourier Transform Analysis

Week 7: 1) filtering and frequency response; 2) BIBO stability; 3) steady state response of stable systems

Week 8: 1) response speed, time constant; 2) frequency response; 3) fundamental concepts of filtering, modulation

Week 9: 1) Laplace transform and continuous-time system analysis; 2) Laplace and inverse Laplace transforms; 3)region of convergence

Week 10: 1) properties of Laplace transform; 2) transform pairs; 3) partial fraction expansion

Week 11: 1) zero-input and zero-state response, modes, poles, zeros; 2) transfer function representation of systems, system block diagrams; 3) analysis of RLC networks & Transform impedance

Week 12: 1) Brief introduction to feedback; 2) Bode plots; 3) pole-zero diagrams