Credits: 4


Prerequisite: Minimum grade of C- in MATH141; and permission of ENGR-Electrical & Computer Engineering department. And minimum grade of C- in ENEE140; or minimum grade of C- in CMSC131.
Restriction: Must be in one of the following programs (Engineering: Electrical; Engineering: Computer).
Credit only granted for: ENEE222, ENEE241, or MATH242.
Formerly: ENEE241.
Discrete-time and continuous-time signals, sampling. Linear transformers, orthogonal projections. Discrete Fourier Transform and its properties. Fourier Series. Introduction to discrete-time linear filters in both time and frequency domains.

Semesters Offered

Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021, Fall 2021

Learning Objectives

  • Interpolate discrete-time sinusoids using knowledge of sampling rate and bandwidth
  • Use complex phasors to represent and manipulate real-valued sinusoids
  • Represent finite-dimensional linear transformations by matrices; interpret the latter in terms of the former
  • Calculate orthogonal projections and least-squares approximations for both real and complex vectors
  • Compute simple low-dimensional DFTs and their inverses from first principles
  • Correctly interpret the information in a DFT spectrum and use it to reconstruct a time-domain signal as a sum of its Fourier components
  • Understand and apply DFT properties pertaining to index reversal, index shift, modulation, periodic extension and zero-padding
  • Compute Fourier series coefficients of simple periodic signals in continuous time
  • Determine the frequency response of a FIR filter; interpret the frequency response in the context of frequency selection
  • Compute the time-domain response of a FIR filter to exponential, periodic and finite-duration inputs
  • Use MATLAB to visualize, analyze and process signals and images, thereby applying the theory and tools taught in the lectures

Topics Covered

  • Real and complex sinusoids in continuous time
  • Sampling of sinusoids, discrete-time sinusoids, aliasing
  • Matrices and linear transformations, linear systems
  • Matrix inversion, Gaussian elimination
  • Inner products, norms, projections; orthogonal bases
  • DFT as an orthogonal projection, interpretation of the DFT
  • Signal transformations and the DFT, symmetry, duality
  • Zero-padded and periodic extensions and the DFT
  • Periodicity in continuous time, sums of harmonically related sinusoids
  • Fourier series of a periodic signal; evaluation of coefficients, properties
  • LTI filters and impulse response, FIR filters
  • FIR filters and finite duration inputs: linear convolution
  • FIR filters with sinusoidal and exponential inputs: frequency response, system function

Learning Outcomes

  • Ability to apply knowledge of math, science, & engineering (Significant)
  • Ability to design/conduct expt. & analyze/interpret data (Moderate)
  • Ability to identify, formulate, and solve engineering problems (Moderate)
  • Techniques, skills, and modern engineering tools necessary for engineering practice (Significant)