Discrete-Time Signals and Systems

Course Description

Discrete-Time Signals and Systems covers difference equations, discrete convolutions, the z transform, discrete and fast Fourier transforms, digital processing of analog signals, the sampling theorem, and probability and random signals.

Within the SCNS taxonomy, EEL is the Electrical Engineering prefix. The University of West Florida publishes this at 3 semester hours through the Department of Electrical and Computer Engineering, College of Science and Engineering. It is offered at approximately 7 Florida institutions.

⚠⚠ The SCNS title for this number is "Signals & Systems"; UWF publishes it as "Discrete-Time Signals and Systems," and the difference is substantive rather than cosmetic. A generic signals and systems course typically spends half its time on continuous-time analysis. UWF's course is scoped to the discrete-time side — difference equations, the z transform, the DFT and FFT — with continuous-time material appearing mainly through sampling. The continuous-time transform work is carried upstream in EEL3112 instead. Students transferring this credit in either direction should carry a syllabus, because a receiving institution matching on the SCNS title will expect content this course does not emphasise, and vice versa.

This is the course that connects the analogue world to everything computational, and the sampling theorem is its central result: a band-limited signal sampled fast enough can be reconstructed exactly, and one sampled too slowly is corrupted in a way no later processing can undo. Aliasing is not noise that can be filtered out afterwards — it is information destroyed at the moment of sampling, and understanding why is the single most transferable idea in the course.

⚠ The contact-hour figure is derived — the University of West Florida publishes none

UWF's catalog publishes a credit value in semester hours, the college and department, prerequisites, and a description. It does not publish contact hours, a lecture and laboratory split, or terms of offering for any course. It does publish a material and supply fee notice on the minority of courses that carry one — and maintains a separate Material & Supply and Equipment Fees section of the catalog — so the absence of a fee notice on this entry is meaningful, while the fee amount is not published here. Every contact-hour value in a UWF guide in this repository is therefore derived. The figure here applies the standard lecture convention of 15 contact hours per credit, giving 45 hours for a 3-semester-hour course. Confirm the meeting schedule with the department.

Learning Outcomes

Required Outcomes

• Represent and manipulate discrete-time signals and standard sequences.
• Classify systems as linear, time-invariant, causal, and stable.
• Formulate and solve linear constant-coefficient difference equations.
• Compute the discrete convolution of two sequences.
• Relate the impulse response to system behaviour and stability.
• Compute the z transform and region of convergence.
• Compute inverse z transforms by partial fractions and by long division.
• Analyse system stability and causality from the pole locations and region of convergence.
• Determine and interpret the discrete-time Fourier transform.
• Compute the discrete Fourier transform and interpret its output correctly.
• Explain the fast Fourier transform algorithm and its computational advantage.
• State and apply the Nyquist sampling theorem.
• Explain aliasing and design anti-aliasing measures.
• Describe quantisation and its effect on signal fidelity.
• Analyse the reconstruction of analog signals from samples.
• Describe and analyse FIR and IIR filter structures.
• Design a simple digital filter to a stated specification.
• Apply basic probability concepts to signals.
• Describe random signals, autocorrelation, and power spectral density.
• Implement discrete-time processing in software.

Optional Outcomes

• Describe multirate processing, decimation, and interpolation.
• Describe windowing and spectral leakage in practical DFT use.
• Describe fixed-point implementation effects.
• Describe adaptive filtering at an introductory level.
• Apply spectral analysis to a real measured data set.

Major Topics

Required Topics

• Discrete-time signals and standard sequences
• System properties: linearity, time invariance, causality, stability
• Difference equations
• Discrete convolution
• Impulse response
• The z transform and region of convergence
• Inverse z transform methods
• Poles, zeros, stability, and causality
• Discrete-time Fourier transform
• Discrete Fourier transform
• The fast Fourier transform
• Sampling and the Nyquist theorem
• Aliasing and anti-aliasing
• Quantisation
• Signal reconstruction
• FIR and IIR filter structures
• Introductory digital filter design
• Probability applied to signals
• Random signals, autocorrelation, power spectral density

Optional Topics

• Multirate processing
• Windowing and spectral leakage
• Fixed-point implementation effects
• Adaptive filtering
• Spectral analysis of measured data

Resources & Tools

• Oppenheim and Schafer, Discrete-Time Signal Processing — the standard reference in the field, and the one most graduate programmes assume.
• Proakis and Manolakis, Digital Signal Processing — the common alternative at undergraduate level, and gentler.
• MATLAB with the Signal Processing Toolbox — check UWF's campus licence before purchasing; the standard tool for this course.
• Python with NumPy and SciPy — free, and scipy.signal covers essentially everything this course needs. A complete MATLAB substitute for coursework.
• GNU Octave — free, and largely MATLAB-syntax-compatible.
• MIT OpenCourseWare 6.003 and 6.341 Discrete-Time Signal Processing — free lectures, the latter taught by Oppenheim himself.
• IEEE Signal Processing Society — student membership is inexpensive and includes the magazine.
• A cheap USB audio interface or a sound card — audio is the most accessible real signal there is, and recording, transforming, and filtering it makes aliasing audible rather than theoretical.

Career Pathways

• Electrical and electronics engineers — SOC 17-2071 and 17-2072.
• Digital signal processing engineering — a specialism in its own right, and the skills here are the entry requirement.
• Radar, sonar, and electronic warfare — the strongest Florida connection. L3Harris (Melbourne and Palm Bay), Lockheed Martin (Orlando), Northrop Grumman (Melbourne) and the naval programmes at NSA Panama City all run substantial DSP work, and Panama City is within UWF's region.
• Communications systems engineering — every modern radio is a DSP problem.
• Audio and acoustics engineering.
• Medical imaging and biomedical instrumentation — MRI, ultrasound, and ECG processing are all applications of this material.
• Machine learning and data engineering — an honest note: the signal processing foundation transfers well, and feature extraction from time-series data is this course's material under another name.
• Embedded systems and firmware — DSP on microcontrollers is a large employment category.

Special Information

⚠⚠ The asterisk in a UWF prerequisite means the course may be taken at the same time

• UWF's catalog marks a concurrent course with an asterisk, defined on the catalog's Course Information page as: "This course may be taken prior to or during the same term."
• ⚠ This is the single most useful piece of notation in the UWF engineering catalog, and it is easy to miss. A prerequisite written without an asterisk must be completed first; one written with an asterisk may be taken in the same term.
• The practical effect is on time to degree. Reading an asterisked prerequisite as a hard prerequisite adds a term to the sequence for no reason, and in a tightly chained major like electrical engineering that error compounds down the whole plan.
• Confirm with an advisor before relying on it, and note that the registration system, not the catalog text, is what actually enforces the rule.

⚠⚠ This course requires programming, and UWF's prerequisite says so explicitly

• UWF requires EEL3112 AND one of EEL4834, COP2253, COP2334, COP3014, or EGN3204. The second branch is a programming course, and the range of accepted options tells you the department cares that you can program, not which language you learned.
• ⚠ Neither branch is asterisked, so both must be completed before enrolling. This is a hard prerequisite chain, unlike EEL3112's partly concurrent one.
• Expect substantial computational assignments. The DFT, FFT, and filter design work is done in software, and a student who is slow at programming will spend their time fighting syntax rather than learning signal processing.
• ⚠ If your programming is rusty, refresh it before the term starts rather than during it. Array indexing, loops, plotting, and reading a library's documentation are the whole requirement.

⚠⚠ Aliasing destroys information, and this is the idea to leave with

• Sampling below the Nyquist rate does not degrade a signal — it corrupts it irreversibly. High-frequency content folds down and becomes indistinguishable from genuine low-frequency content.
• ⚠ No amount of later processing recovers it. This is the crucial engineering consequence, and it is why the anti-aliasing filter sits before the converter in every real system.
• The wagon-wheel effect in film is the everyday example, and audio sampled at too low a rate is the audible one. Generate both yourself; it takes ten minutes and it fixes the concept permanently.
• ⚠⚠ Nyquist is a strict inequality and real systems need margin. Sampling at exactly twice the highest frequency works in the theorem and fails in practice, because ideal brick-wall filters do not exist.

⚠ The DFT is not the Fourier transform, and conflating them causes real errors

• The DFT operates on a finite record and implicitly assumes that record repeats periodically. When it does not — which is nearly always — the result shows spectral leakage.
• ⚠ Frequency resolution is set by the record length, not by the sampling rate. Students routinely try to improve resolution by sampling faster, which does not work; a longer record is what is needed.
• Zero-padding interpolates the display and adds no information. It makes a spectrum look smoother without resolving anything new, and this is a common misreading.
• Windowing trades leakage against resolution. There is no window that wins on both, and choosing one is an engineering decision rather than a default.
• ⚠⚠ The FFT is an algorithm, not a transform. It computes the DFT efficiently. Saying "take the FFT of the signal" is idiomatic and describes computing a DFT.

⚠ Workload and preparation

• Demanding, and comparable to Circuits II — budget 8 to 12 hours a week outside class.
• The z transform will feel familiar if Laplace was learned properly and alien if it was not. The structural parallel is exact, and students who memorised Laplace rather than understanding it pay for that here.
• Probability arrives late and is frequently underestimated. The random-signals unit is a genuine topic shift, and students who have not had a probability course should expect to work at it.
• Build intuition with plots. Nearly every concept in this course has a visual form, and students who plot everything understand it faster than those who work purely symbolically.

FE exam relevance

The Fundamentals of Engineering (FE) exam is the first step toward Professional Engineer licensure, and in Florida it is administered under the Florida Board of Professional Engineers. Most students take the FE Electrical and Computer exam in their final year. Licensure matters less in electrical engineering than in civil — the industrial exemption means most electrical engineers in manufacturing and product work never need a PE — but it is required for consulting practice, for sealing designs, and for power and building-systems work, which is exactly where Florida's utility and infrastructure employment sits.

Course format and position in the curriculum

• Lecture with problem sets and computational assignments.
• Typically taken in the third year, after Circuits II, and it gates communications and control work — EEL4510 Communication Networks lists this course as its prerequisite.
• UWF publishes no contact hours, lecture and laboratory split, or terms of offering for any course, and no material and supply fee is noted on this entry. Confirm the offering pattern with the department.

How Florida course levels affect transfer

The first digit of an SCNS number denotes the year of offering, not transferability. Courses at the 1000 and 2000 levels transfer transparently between Florida public institutions, and 3000 to 4000 is unproblematic since both are upper division. The boundary that actually matters is 2000 to 3000, where lower-division credit generally cannot satisfy an upper-division requirement. ⚠ For engineering specifically, ABET-accredited programmes commonly require that upper-division engineering coursework be taken in residence, so transferability of the credit and applicability to the degree are separate questions.

EEL3135 is 3 semester hours at the University of West Florida. Because the SCNS title ("Signals & Systems") is broader than the local title and the local scope, students transferring credit should carry a syllabus.