ECE 345 Fall 2020

Welcome to ECE 345:  Linear Systems and Signals!

Make sure you have a solid grounding with the Prerequisite Skills Checklist. There is information about the teaching philosophy behind this course and what it takes to master this material. This course is designed around a set of Learning Outcomes. To get a sense of how well you are doing in the class (and whether you are prepared for the exam) is to go through the objectives and see if you can do those things.

Throughout the semester, we will communicate with you via either Canvas Announcements or your Rutgers email account. Please review the information for Accessing Rutgers Email:

Note: Almost all original work is the intellectual property of its authors, which for this class may include the authors of the Ulaby and Yagle, Lathi and Green, Oppenheim and Willsky, and others references in the course material. These works may include syllabi, lecture slides, recorded lectures, homework problems, exams, and other materials, in either printed or electronic form. The authors may hold copyrights in these works, which are protected by U.S. statutes. Copying this work or posting it online without the permission of the author may violate the author's rights. More importantly, these works are the product of the author's efforts; respect for these efforts and for the author's intellectual property rights is an important value that members of the university community take seriously.


Anand D. Sarwate (, Office Hours: Wednesday/Friday 12-1:20 PM
Salim El Rouayheb (, Office Hours: Tuesday 4:00 PM - 6 PM

Teaching Assistants:
Jiazhen Hong (, OH: Thursday 1:30 PM - 3:30 PM (EST)
Carolina Naim (, OH: Wednesday 3:30 PM - 4:30 PM, Thursday 9:30 AM -10:30 AM  (EST)
Ye Tao (, OH: Monday 4:00 PM - 6:00 PM (EST)
Vahideh Vakil (, OH: Tuesday 12:00-2:00 PM (EST)

More information about the instructors is available. We will be all holding office hours throughout the semester.

Meeting Times

This course is designated as asynchronous remote. The course is organized into weekly Modules.

Course Description

Signals are everywhere: there are audio signals in our earbuds, WiFi signals going to our laptops, and image signals taken by our smartphones. Signals can be optical (images, fiber optics), acoustic (music, sonar), physical (earthquakes, pressure), and electrical (voltage, current). How can we understand this diversity of signals in a unified framework? This class develops that unified framework so that we can understand key properties of signals in terms of mathematics. This mathematical modeling lets us use computational tools to analyze, process, and manipulate signals. A key feature of this mathematical theory is the Fourier Transform, which lets us understand signals in terms of different frequencies. As a simple example, there are high (treble) and low (bass) frequencies in music.

We can manipulate these signals using systems. In order to design complex systems it's helpful to be able to build them out of simpler components. If we characterize a system by how it transforms an input signal into an output signal, we can start to compose systems. A linear system is one which acts linearly on its inputs, so doubling the amplitude of the input would double the amplitude of the output and making the input the sum of two signals produces the sum of the two corresponding outputs. A time-invariant system is one for which delaying the input by an amount will delay the output by the same amount. Linear time-invariant (LTI) systems are easy to compose, and we can also use the Fourier Transform to understand them; LTI systems transform input signals by scaling different frequencies. As an example, an LTI system going to a subwoofer scales high frequencies down to isolate the low frequencies.

LTI systems and signals are the foundation for communications, control, and signal processing. Communication systems have to designs signals that are resistant to noise. LTI systems model the communication link between the transmitter and receiver. Control systems use feedback to stabilize systems ranging from airplane wings to amplifiers to power plants. Modern digital cameras are full of signal processing algorithms to do things like motion correction, autofocusing, and a plethora of other tasks. In this class we will build this mathematical foundation to open the door to these and other exciting applications.


Prerequisites: Principles of EE 2 (ECE 222/224), Differential Equations (Math 244, 252, or 292)

Technology requirements: MATLAB, a camera/scanner, high-speed internet to support video lectures.


Learning outcomes:

Textbooks and resources:

  • The lecture notes are handwritten PDF notes first used in 2017. The notes refer to the textbook by Oppenheim and Willsky, which is not a required text (it was in 2017).
  • Video lectures for the course will be posted on the ECE 345 YouTube Playlist and also embedded in each Module.
  • We have additional resources including a free supplementary textbook

Teaching Philosophy

Even though this course is typically taken in students' junior or senior year, this course is a foundational course for an entire area of ECE, including digital signal processing, communication systems, control systems, and even machine learning. At its heart, this is an applied mathematics course, where the applications are in engineering. Why do we need all of this math? We need it to provide an explanation of how systems work (like circuits) that lets us analyze potential designs for more complex systems in order to choose the best one. As an example, there are many ways to implement a communication signaling scheme: what are the tradeoffs (e.g. cost, power) between the different designs? This is math with a purpose.

The major objective of the course is for students to become fluent in modeling and analyzing signals (data, measurements) and systems (sensors, actuators, filters). In order to gain this fluency, students have to move from understanding basic definitions and concepts to applying them. Mastering this material requires practice: we give some examples to try at the end of many lectures and formative assessments (check-ins, homeworks) are designed to help set up a scaffold for students to practice on their own. Summative assessments (quizzes, labs) will check how fluent students have become.

At the same time, building complex technologies requires engineers to work in teams. We will group students randomly into teams to work on the lab assignments, which will involve implementation and simulation of the material from class in MATLAB.  Each lab will have a different team and we anticipate that teams will also form study groups. Group work is even more important due to our asynchronous remote instruction format: with COVID-19 and social distancing, we want to make sure that students don't become isolated.

Assessments and Grading

Course expectations

We expect students will spend 9 hours per week on this course, assuming that they space the work on the labs over the course of several weeks. Discussions and questions will be on Piazza: we expect students to make good use of this tool to help answer questions during the semester. To succeed in this class students should be able to contribute to group work as well as show that they individually understand the course material.

Academic Policies and Procedures

Course Summary:

Date Details Due