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ECE210

ECE210 (Analog Signal Processing) is a 4 credit hour course that is specifically required for all ECE majors as part of the Electrical and Computer Engineering Core Curriculum. It is offered in the fall, spring, and summer semesters.

Content Covered

  • Basic circuit analysis
  • Complex numbers
  • Superposition and linearity
  • Ideal op-amps
  • Linear time-invariant systems
  • Transient and steady-state responses
  • Phasors
  • Frequency response
  • Fourier series
  • Fourier transform
  • Signal bandwidth
  • Amplitude modulation, coherent demodulation, envelope detectors
  • Sampling, reconstruction of analog signals
  • Convolution
  • Dirac delta function, impulse response of LTI systems
  • Causality, BIBO stability of systems
  • Laplace transform, transfer functions

ECE210 is, for most students, the first real synthesis of electrical engineering and mathematics. The first part of the course covers basic circuit analysis. This includes Thevenin and Norton equivalent circuits, source transformations, the node voltage method, the loop current method, superposition, and circuits with ideal op-amps. Complex numbers are reviewed, including Euler’s formula and the exponential form of sine and cosine.

ECE210 then moves on to analysis of RL and RC circuits. Students will learn to solve differential equations to determine voltages and currents and RL and RC circuits. The concept of a linear time-invariant (LTI) system is introduced, and students will learn to determine the transient and steady-state responses of LTI systems. They will recognize that an analog circuit is an LTI system with inputs being voltage and current sources and outputs being voltages and currents. Phasors are introduced, which simplify computations immensely. Using phasors, students can understand the concepts of impedance and frequency response.

The course becomes increasingly mathematical when the Fourier series and Fourier transform are introduced. Using the Fourier series, students will be able to determine the steady-state response of an LTI system to any periodic input. The Fourier transform allows for representation of aperiodic signals in the frequency domain, leading students to be able to determine the steady-state response of an LTI system to aperiodic inputs. Electrical engineering majors will find many future uses of Fourier transforms and should master their understanding of the topic. For example, the Fourier transform and its modulation property have applications to AM radio, which are discussed in lecture and expanded upon further in the lab.

Students will then learn convolution, the Dirac delta function, and the impulse response of an LTI system. Convolution allows for an alternative method of determining the steady-state response of an LTI system, that is, by convolving the system input with the system’s impulse response. The Dirac delta function also has applications to sampling and signal reconstruction, which are covered in ECE210. The concepts of causality and bounded-input, bounded-output (BIBO) stability for LTI systems and their relations to the system’s impulse response are then covered.

Finally, the Laplace transform is introduced, which converts signals to the s-domain. Using the Laplace transform, students will be able to determine the transfer function of a linear, time-invariant, causal (LTIC) system. Analysis of LTIC circuits in the s-domain is covered, allowing students to determine the general response of an LTIC system.

To complement the material covered in lecture, lab work involves the development of an AM radio receiver. In each lab, students construct and analyze a component of the receiver using an ADALM-2000 as an oscilloscope, function generator, and power supply.

Prerequisites

ECE110, PHYS212, and credit or concurrent registration in MATH285 are listed as official prerequisites of this course. Although MATH285 can be taken concurrently, it is recommended to take it beforehand, if possible, as ECE210 relies heavily on the ability to solve differential equations. A student that takes them concurrently might have to learn some topics in ECE210 before MATH285, which can be tricky. Fourier series and transforms, for example, are covered in ECE210 before they are covered in MATH285. Note that there are slight differences in methods used for many overlapping topics between MATH285 and ECE210 which make these courses somewhat challenging to take concurrently. For example, ECE210 teaches Fourier transforms in terms of strictly complex numbers, while MATH285 reduces these expressions to real sine and cosine functions.

Relevant topics from ECE110 include DC circuit analysis - Thevenin and Norton equivalents, the node-voltage method, and source transformations - and lab work involving breadboards, oscilloscopes, and function generators. An understanding of basic AC circuit analysis, i.e., voltages and currents in RC, RL, and LC circuits, resonance, and phasors from PHYS212 is also important. In MATH285, paying extra attention to topics of first order solutions, Fourier series, Fourier transforms, and Laplace transforms will come in handy.

When to Take It

Students interested in electrical engineering should take ECE210 as soon as possible. It is strongly recommended for electrical engineering majors to take this course by the second semester of their sophomore year to graduate in time. ECE210 is the backbone of the electrical engineering curriculum as it covers fundamental concepts used in almost every upper level electrical engineering course. It is a prerequisite for many required and elective intermediate electrical engineering courses, including ECE310, ECE329, ECE330, ECE340, and ECE342. While ECE210 largely covers introductory circuit analysis and analog signal processing, the course also develops one's intellectual maturity applicable in other areas of electrical engineering. Computer engineering students can be a bit more flexible with when they take this class, but should still take it sooner rather than later in order to open up future elective and upper level coursework. To take ECE210 as soon as possible, start taking required MATH and PHYS courses right away, so that you are able to take MATH285 and PHYS212 as soon as possible.

Course Structure

ECE210 has a fairly heavy workload and is also conceptually difficult. Expect this course to be more difficult than any other course you have taken before.

ECE210 is unusual in that it meets four times a week for lecture. Lecture attendance is not required but is recorded using iClickers, with students who attend at least 76% of lectures being allowed to retake quizzes. Some topics may require more than one lecture, sometimes even three, to fully cover one section of the chapter. Don’t be fooled, this class moves at a fast pace consistently, and requires you to have a strong comfort level with material every day. It can be easy to fall behind if you stop attending lectures.

Homework is assigned weekly. Homework assignments take up a decent amount of time, and usually cover the material of the current week and the week prior. Since this class builds on from each chapter to the next, understanding how to do the homework problems is your key to success. Note that each chapter contains many examples that are comparable to homework problems. Making an effort to fully understand the concepts behind every problem will shorten the amount of time required to prepare for quizzes and exams.

ECE210 also has three quizzes, held at the CBTF in between midterm exams. To prepare for these quizzes, students are recommended to go over past homework problems.

In addition to the homeworks and quizzes, ECE210 also has three midterm exams and a final exam. These exams, especially the second and third midterms and the final exam, are challenging and typically have low average scores. Exams reflect material covered in homework, but most likely will contain 1 or 2 tricky problems that test the student's ability to apply concepts to unfamiliar situations. Students are not allowed a calculator or cheat sheet and are only provided with specific tables from the textbook. Thus, doing well on the exams will require an excellent understanding of the relevant concepts. Practicing past exam problems and the homeworks will help one perform well on exams, as will reading the textbook.

Finally, ECE210 also has a lab component, focusing on the real-world applications of concepts covered in lecture, of which there are many. Lab meetings are biweekly and do not begin until one month into the semester. One week before the lab section meets for demos, a short prelab assignment is due. The prelab assignments are not too difficult and are meant to review necessary concepts from lecture for the upcoming lab. There are a total of five lab assignments in ECE210. For each lab assignment, students will fill out a worksheet. The worksheets require the student to build circuits, take measurements of their circuits using the ADALM-2000 and Scopy software, including measuring frequency response and Fourier coefficients, and plot signals in the time and frequency domains. During the lab section, students are expected to demo their circuit to the TAs or CAs and answer one to two questions regarding the relevant concepts. Much of the lab covers the application of signal processing to AM radio. In the labs, students will construct an envelope detector, amplifier circuits, and an active filter before combining them to build a work AM radio receiver. The final lab covers sampling of continuous time signals, requiring the use of Python.

An additional weekly honors section led by upperclassmen is also available to students who want to use Python for course relevant material. The honors section consists of a weekly one hour tutorial/demo section where students are taught about Python concepts related to signal processing. The student must then complete a Jupyter Notebook assignment that can take two to five hours, depending on the week. Completing the six Python assignments will earn a James Scholar student honors credit. The honors section is a good way to learn introductory Python skills, and is very helpful if students intend to take ECE311 or ECE314, the accompanying labs for ECE310 and ECE313, respectively.

Note that the course structure of ECE210 often varies slightly from semester to semester. For the most up to date information, view the syllabus or the course website.

Instructors

This course is currently directed by Professor Kudeki. Instructors vary from semester to semester and typically have backgrounds in a wide variety of fields of electrical engineering, namely signal processing, communications, electromagnetics, power systems, and solid-state electronics. Professors who have taught ECE210 recently include Professors Alvarez, Schmitz, Waldrop, Lee, Mironov, Mironenko, Chen, Schuh, Shao, and He. Professor Alvarez has taught this course every semester since Fall 2019.

Course Tips

ECE210 is a challenging course. Do not skip lectures, as this will only require you to spend more time later to catch up on the material. Falling behind can make it much more difficult to do well in the class. While in lecture, take good notes and ask good questions. Consistency is key for this class. Being consistent with asking questions to your professors, reading up on the material, taking notes, whatever helps you learn best - as long as you are consistent, you can succeed in this course!

Now is the time to form good study habits. Start homework early. If you get stuck, consult your notes and the textbook, and go to office hours. Even if you feel like you understand the content, going to office hours is still a good idea, as other students may ask questions you haven’t considered before. In addition to lectures, read the textbook often. This will allow you to pick up on topics you may have missed during lecture. The textbook also contains many practice problems that are similar to the homework problems, which can help you gain a deeper understanding of the material.

Many past exams are posted on the course website, dating back to 2007. Going through the past exam problems is one of the best ways to study for the midterm and final exams. However, simply looking over the solutions for past exams will not help at all. Past exams are truly useful if they are taken in an exam environment (and if you only check solutions after truly attempting the problem).

The professors have started to run small discussion sections on Thursdays and Fridays that you have to sign up for in advance, with the groups being limited in size. During these sessions, you will work on extra problems and walk through them with the professors or TA's. These discussion sections are the most useful resources available. Sign up for these, especially if you are struggling in the course!

Life After

ECE210 is the foundation of the electrical engineering curriculum and is the prerequisite to many intermediate and advanced level ECE courses. Electrical engineering majors are recommended to take ECE329 - Fields and Waves I the semester after taking ECE210 as it is a required course for EEs and the next step in the EE Core Curriculum. ECE329 is the introductory course in electromagnetics, covering important, fundamental topics such as Maxwell’s equations, wave propagation, transmission lines, and impedance matching. ECE329 requires a good understanding of phasors and lumped circuit analysis from ECE210.

Students who enjoyed the signal processing portion of ECE210 should consider ECE310 - Digital Signal Processing. While ECE210 focuses on continuous-time signal processing, ECE310 focuses on discrete-time signal processing. Many of the topics covered in ECE210, including linearity, causality, stability, convolution, and Fourier transforms, will also be covered in ECE310, but in the digital domain. Sampling and reconstruction of analog signals will also be covered in much more detail in ECE310.

For students who enjoyed the signal processing portion and wish to pursue signal processing further, it is also recommended to take ECE313 - Probability with Engineering Applications the semester after taking ECE210. ECE313 is another mathematically heavy course that is required for all ECE majors, covering probability theory. ECE210 and ECE313 will prepare students for advanced courses in the field of signal processing and communications systems, including ECE459 - Communications Systems and ECE461 - Digital Communications. ECE459 and ECE461 expand upon many concepts taught in ECE210, including Fourier transforms, convolution, amplitude modulation, bandwidth, and linear time-invariant systems. ECE459 largely covers analog modulation schemes as well as some digital modulation techniques and topics related to probability, namely, random processes and signal to noise ratio. ECE461 largely covers modeling of digital communications systems, discussing the communication of bits over additive Gaussian noise, wireline, and wireless channels.

Students who enjoyed the circuit analysis portion of ECE210 should consider ECE342 - Electronic Circuits. ECE342 covers circuit analysis and design with nonlinear components - diodes, MOSFETs, and BJTs - and largely focuses on amplifiers. In this course, among other topics, students will learn to graph Bode plots and estimate transfer functions of amplifiers, building off of concepts introduced in ECE210.

Students who enjoyed the circuit analysis portion of ECE210 should also consider ECE330 - Power Circuits and Electromechanics. ECE330 covers circuits relevant to the power field, relying on a student’s knowledge of phasors, RMS values, and complex numbers. In ECE330, students will learn three-phase circuit analysis, wye and delta connections, the wye-delta transform, and the equivalent circuits of transformers, synchronous machines, and induction machines. An understanding of the stability of systems will also be relevant for ECE330.

Along with PHYS214 and credit or concurrent registration in ECE329, ECE210 is a prerequisite for ECE340 - Semiconductor Devices, a required course for electrical engineering majors. Though ECE340 has little overlap with ECE210 itself, focusing more on the physics of semiconductor materials and devices, students who liked their prior physics courses, especially PHYS213 and PHYS214, could consider specializing in solid-state electronics and taking ECE329 and ECE340 concurrently the following semester.

Finally, ECE210 is also a prerequisite for ECE486 - Control Systems. Controls is a field closely related to signal processing and has to do with the regulation of systems to ensure desired behavior using feedback. ECE486 is the introductory course in controls, using many topics introduced in ECE210 such as system stability and the Laplace transform and applying them to feedback control systems.

Students should develop a better idea of their academic interests after taking this course. Generally, students who dislike this class do not intend to pursue electrical engineering as a major. However, be aware that ECE210 is only the tip of the iceberg of electrical engineering, and not liking this course does not necessarily indicate disinterest. This course will give the electrical engineering student a better idea on what to specialize in, as well as aid in the choice of technical electives (especially those in the 3-of-5 for EE majors and the 1-of-6 for CompE majors).

Infamous Topics

  • Fourier series, Fourier transform: This is among the most difficult and math-heavy topics in the course, though it is also the most applicable. For this reason, it is highly recommended for students to study this fully to be prepared for future electrical engineering courses.
  • Convolution: Performing convolutions using the integral method can be computationally difficult. Students should be familiar with graphical convolution and should use this method whenever possible.
  • Laplace transform: Along with the Fourier transform, the Laplace transform is a concept that requires an excellent understanding of foundational mathematics, especially differential equations.

Resources

The textbook for ECE210, Analog Signals and Systems, is co-authored by the course director, Professor Kudeki. It is an excellent supplement to lectures and provides many practice problems which can be helpful for studying for quizzes and exams.