Fourier Methods in Digital Signal Processing - ME57900

April 28, 2026

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Alternate Title: Fourier Methods in Digital Signal Processing Fundamentals of signal processing associated with Fourier analyzer systems are presented. Emphasis is on amplitude accuracy and frequency resolution properties necessary for reliable experimental methodologies in system identification, spectrum estimation, and correlation analysis. Deterministic as well as random data analyses are presented.

Credit Hours: 3

Instructor(s): Yangfan Liu

Email: yangfan@purdue.edu

Learning Objective:

To familiarize the student with functions found in most frequency analysis software, introduce the basics of digital filtering and digital filter design, introduce basis of stationary signal analysis and derive input-output relationships for linear time-invariant systems.

Description:

Alternate Title: Fourier Methods in Digital Signal Processing Fundamentals of signal processing associated with Fourier analyzer systems are presented. Emphasis is on amplitude accuracy and frequency resolution properties necessary for reliable experimental methodologies in system identification, spectrum estimation, and correlation analysis. Deterministic as well as random data analyses are presented.

SP2018 ME57900 Syllabus

Topics Covered:

Engineering applications of Fourier analysis of signals, both random and deterministic; Digital Filtering; Spectral estimation; Transfer function estimation; Coherence; Effects of measurement (windowing, sampling, noise); Strategies to minimize adverse effects and to facilitate meaningful interpretation of data analysis results

Prerequisites:

Undergraduate treatment of Laplace transforms, Fourier series, basic statistics.

Applied / Theory:

30 / 70

Web Address:

http://engineering.purdue.edu/ME579

Homework:

Seven homework assignments, each consisting of 5 questions. Please keep each problem separate, i.e. start a new problem on a new sheet of paper, and make sure your name and the problem set and problem number are on each sheet of your solutions.

Projects:

None

Exams:

One midterm exam and one final exam.

Textbooks:

Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Required-None. List of recommended reference texts will be provided with the course syllabus.
Disclaimer: Please visit the Listing of Textbooks by College or School for the most up-to-date textbook information.

Computer Requirements:

ProEd minimum computer requirements, Pentium or equivalent required, 0.1 Gigabytes of disk space, MATLAB with the signal processing toolbox; extensive use of MATLAB, including use of MATLAB programs and programming of specific algorithms used during homeworks (note: some functions used during class are not available in the student edition of MATLAB); must be compatible with Microsoft packages; course outline and information, homeworks and solutions, signals for downloading for some homeworks, sample exams and exam solutions, pointers to course references and exam announcements will be posted on the course web site.

ProEd Minimum Requirements:

As noted previously, access to MATLAB and the signal processing, system identification and statistics toolboxes.