Credits: 4

### Description

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, Spring 2022, Fall 2022

### 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)