## ENEE222 Elements of Discrete Signal Analysis

#### Course Description:

The course begins by covering basic tools for signal analysis, namely real and complex sinusoids in both discrete and continuous time, sampling, linear transformations and orthogonal projections. It then develops the discrete Fourier transform (DFT) in detail and also provides an introduction to Fourier series. The course concludes with a discussion of FIR filters whereby key ideas and methodologies in linear time-invariant systems such as convolution (linear and circular), system functions, and frequency-selective filtering are presented.

#### Prerequisite(s):

MATH141; ENEE140 or CMSC131 (Credit only granted for: ENEE222, ENEE241, or MATH242. Formerly: ENEE241.)

None

#### Course 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)