ECEN 314 – Signals and Systems
About the course
ECEN 314 introduces the mathematical tools used to describe signals and to analyze the systems that act on them. We work in both continuous and discrete time, and the course builds toward a single idea: a linear time-invariant (LTI) system is completely characterized by its impulse response, and transform methods turn the hard operation of convolution into ordinary multiplication.
Instructor - Sanjana Kunkolienkar Term - Fall 2026 Lecture - MWF, 1:50PM-2:40PM.
Lectures
Slides are posted after each lecture. The course runs 41 class days across 15 weeks, organised into the units below.
| # | Topic | Materials |
|---|---|---|
| Mathematical Foundations | ||
| 1 | Math review — complex numbers, Euler's formula & geometric series | |
| Signals | ||
| 2 | What is a signal? | |
| 3 | Signal energy, power & periodicity | |
| 4 | Signal transformations (shift, scale, reflect) | |
| 5 | Even/odd symmetry & the exponential/sinusoid family | |
| 6 | Impulse & step signals; the sifting property | |
| Systems | ||
| 7 | What is a system? Theme examples | |
| 8 | System properties: linearity & time invariance (part 1) | |
| 9 | System properties: causality, memory, stability, invertibility (part 2) | |
| Time-Domain LTI Analysis — Convolution | ||
| 10 | Impulse response & deriving the DT convolution sum (part 1) | |
| 11 | DT convolution — the graphical procedure & examples (part 2) | |
| 12 | The CT convolution integral (part 3) | |
| 13 | Convolution properties & reading LTI properties from h(t) (part 4) | |
| Continuous-Time Fourier Series | ||
| 14 | Complex exponentials as eigenfunctions; the FS idea | |
| 15 | Computing FS coefficients — the direct method (part 1) | |
| 16 | FS by inspection & convergence (part 2) | |
| 17 | CTFS properties [last topic on Midterm 1] | |
| R | Review for Midterm 1 | |
| M1 | Midterm 1 — Signals, Systems, Convolution & CT Fourier Series | |
| Continuous-Time Fourier Transform | ||
| 18 | LTI response to periodic inputs & filtering | |
| 19 | From FS to the CTFT; transforms of basic signals | |
| 20 | CTFT properties — core set (part 1) | |
| 21 | Convolution–multiplication property & Parseval (part 2) | |
| 22 | Frequency response, filtering & inverse transform | |
| 23 | Application: AM modulation & demodulation | |
| Discrete-Time Fourier Analysis | ||
| 24 | Discrete-Time Fourier Series (DTFS) | |
| 25 | Discrete-Time Fourier Transform (DTFT) | |
| 26 | DT frequency response & digital filters | |
| 27 | DT Fourier examples & consolidation [last topic on Midterm 2] | |
| R | Review for Midterm 2 | |
| M2 | Midterm 2 — CT Fourier Transform & Discrete-Time Fourier | |
| Sampling | ||
| 28 | The Sampling Theorem & impulse-train derivation (part 1) | |
| 29 | Aliasing & reconstruction (part 2) | |
| 30 | Discrete-time processing of CT signals | |
| Laplace Transform | ||
| 31 | Why another transform? Definition & the s-plane (part 1) | |
| 32 | Region of convergence, poles & zeros (part 2) | |
| 33 | System analysis & stability via Laplace (part 3) | |
| 34 | Feedback control & the unilateral Laplace transform (part 4) | |
| Review & Final Exam | ||
| R1 | Review Day 1 — first half (Units 0–5) | |
| R2 | Review Day 2 — second half (Units 6–8) | |
| R3 | Final review — cumulative | |
| F | Final Exam — cumulative · Wed Dec 9, 3:30–5:30 PM | |
Homework
Six graded problem sets, together worth 20% of the course grade. Each is due at the start of class on the date listed, before the exam that covers it.
| HW | Topic | Covers | Assigned | Due | Materials |
|---|---|---|---|---|---|
| 1 | Math review + Signals | Lec 1–6 | Sep 4 | Sep 11 | |
| 2 | Systems + Convolution | Lec 7–11 | Sep 11 | Sep 18 | |
| 3 | CT Convolution + FS intro | Lec 12–14 | Sep 18 | Sep 25 | |
| 4 | CTFT + AM | Lec 18–23 | Oct 16 | Oct 23 | |
| 5 | DT Fourier | Lec 24–27 | Oct 23 | Oct 30 | |
| 6 | Sampling + Laplace | Lec 28–34 | Nov 13 | Nov 20 |