Signals and Systems

(3-0-0-3)

CMPE Degree: This course is Selected Elective for the CMPE degree.

EE Degree: This course is Selected Elective for the EE degree.

Lab Hours: 0 supervised lab hours and 0 unsupervised lab hours.

Technical Interest Groups / Course Categories: Threads / ECE Electives

Course Coordinator: Yorai Wardi

Prerequisites: ECE 2026 [min C] and (ECE 2040 [min C] or (ECE 3710 [min C] and MATH 2403 [min C] and MATH 2413 [min C] and MATH 24X3 [min C]) or (ECE 3710 [min C] and MATH 2552 [min C] or MATH 2562 [min C] or MATH 2X52 [min C]) )

Catalog Description

Continuous-time linear systems and signals, their mathematical representations, and computational tools; Fourier and Laplace transforms, convolutions, input-output responses, stability.

Textbook(s)

Signals and Systems, myDAQ, myDAQ unit

Course Outcomes

Express continuous-time signals in mathematical form

Define and apply the Fourier transform

Analyze signals in terms of their frequency contents

Describe system behavior in terms of the Fourier transform 

Apply the Laplace transform 

Solve linear, ordinary differential equations using the Laplace transform

Derive transfer function representations of linear systems

Relate system stability to the properties of the transfer function

Explain the role of feedback in linear systems 

Describe how continuous-time signals and systems are used in engineering applications

Strategic Performance Indicators (SPIs)

N/A

Topic List

  1. Introduction and motivation
    1. Engineering approximations and mathematical abstractions
    2. Continuous-time vs. discrete-time signals and systems
    3. Linear systems (superposition)
    4. Time invariance
  2. Frequency-domain signal analysis
    1. Fourier series
    2. Continuous-time Fourier transforms
    3. Properties of Fourier transforms
  3. Frequency-domain characterizations of linear systems
    1. Transfer functions (jw)
    2. Frequency responses
  4. Time-domain characterizations of linear systems
    1. Differential equations
    2. Convolution
    3. Lumped vs. distributed systems
  5. Discrete-time representations of continuous-time signals
    1. Nyquist sampling
    2. Filters (A/D -> filter -> D/A cascade)
  6. Laplace-domain signal analysis
    1. Forward and inverse Laplace transforms
    2. Properties of Laplace transforms
    3. Initial and final value theorems
    4. Convolutions
    5. Connections between Fourier and Laplace transforms
  7. Laplace-domain characterizations of linear systems
    1. States
    2. Laplace-domain representation of ODEs
    3. Transfer functions (s); poles and zeros
    4. Responses (zero state, zero input)
    5. Laplace-domain electric circuit analysis
    6. Stability
    7. Feedback

Typical in-class labs may include:

  1. Sensing and data filtering
  2. Proportional feedback design
  3. Signal generation and frequency analysis