ECE3084B: Signals and Systems (Fall 2012)

# ECE3084B: Signals and Systems (Fall 2012)

**Instructor:**

Aaron Lanterman (office Van Leer W431; e-mail lanterma@ece.gatech.edu —

if you e-mail me about anything related to the class please put “3084” in the

subject line)

**Teaching assistant:** TBD

**When:** TuTh 12:05-1:25

**Where:** Bunger Henry 311

**Course description:** Continuous-time linear systems and signals, their mathematical representations, and computational tools. Fourier and Laplace transforms, convolutions, input-output responses, stability.

The subject area of signals and systems is perhaps the most important in all of science and engineering in that it provides the abstractions that allow us to reason about pretty much everything – from electrical circuits to self-driving cars. This course investigates signals and systems via Fourier and Laplace transforms, linear systems theory, and applications drawn from many aspects of electrical engineering.

**Prereqs:** (ECE2025 or ECE2026) and ECE2040

## Schedule

It’s unlikely that the listed topics will match up exactly on the listed dates.

This is just a rough estimate of how the material will flow to give you a sense

of where we are headed. The readings are “suggested.”

(A 0 at the end of a number,

for instance 3.7.0, means that we suggest that you read staring with

the Section 3.7 header, but not necessarily go into Section 3.7.1)

- 1/8 – Introduction;

course outline;

signals as functions; unit step and Dirac delta functions (Chen, Sec. 1.3-1.5) - 1/10 – Systems; linearity (Chen, Sec. 2.4 — but note that for now

we are dealing with initial conditions, i.e. we are dealing with

what Chen calls “zero-state response” or “forced response”),

time-invariance (Chen, Sec. 2.5),

and causality (Chen, Sec. 2.2) - 1/15 – Impulse response; convolution (Chen, Sec 3.7.0);

why LTI systems are important (Chen, Sec. 2.6) - 1/17 – “Graphical” convolution (Chen, Sec. 3.7.2)
- 1/22 –
**Optional**convolution practice - 1/24 – Review of Fourier series (Chen, Secs. 4.1.1, 4.2.0-4.2.1)
- 1/29 – Fourier transforms, part 1 (Chen, Sec. 4.3, 4.4.0)
- 1/31 – Fourier transforms, part 2
- 2/5 – AM modulation (Chen, Sec. 8.7), baseband signal representations
- 2/7 –
**Quiz 1**(covers lectures from 1/7 through 1/31) - 2/12 – Fourier view of sampling theory (Chen, Sec. 5.3)
- 2/14 – Relation between various transforms;

Fourier series reimagined as frequency-domain sampling - 2/19 – Parseval’s theorem and applications (Chen, Secs. 4.2.2, 4.4.1)
- 2/21 – Lab 1: Guitar strings as linear systems
- 2/26 – Introduction to Laplace transforms (Chen, Sec. 6.2, 6.4)
- 2/28 – 1st and 2nd order ODEs (Chen, Sec. 6.3.1);

inverse Laplace transforms; simple partial fraction expansions

(Chen, Sec. 6.5.1) - 3/5 – Laplace-domain electric circuit analysis (Chen, Sec. 6.3.2)
- 3/7 – Stability (Chen, Sec. 6.7.0); poles-zeros (Chen, Sec. 6.3.4, 6.6);

general partial fraction expansions (Chen, Sec. 6.5.2-6.5.3) - 3/12 – Systems; block diagrams;

transfer functions (Chen, Sec. 6.3.0-6.3.1) - 3/14 –
**Quiz 2**(covers lectures from 2/4 through 3/6) - 3/26 – Frequency response (Chen, Sec. 6.8);

relation to Fourier transform (Chen, Sec. 6.9) - 3/28 – Time & frequency responses of 2nd order systems (Chen, Sec. 6.10)
- 4/2 – Filter design and implementation (Chen, Sec. 6.8.2);

link between Laplace transforms and Z transforms (Chen, Sec. 9.2.1) - 4/4 –
**Lab 2: Frequency response of state variable filter circuits** - 4/9 – Introduction to control; open/closed loop;

feedback (Chen, Sec. 8.4.0); P controller - 4/11 – PI controller; limitations of PI control
- 4/16 – PID controllers (Chen, pp. 301-302); pole placement
- 4/18 – Feedback in circuit design/analysis (Chen, pp. 297-300,

Sec. 8.4.2); implementation - 4/23 –
**Lab 3: PID motor control** - 4/25 – Review for Final Exam

<!–

- 9/11: Properties of Fourier transforms
- 9/13: Convolutions and impulse responses
- 9/18: Frequency response v. 1; review for Quiz 1
- 9/20:
**Quiz 1** - 9/25: Frequency spectra in discrete time; Nyquist sampling
- 9/27:
**Lab 1: Fourier and guitar strings** - Laplace transforms
- 10/2: Differential equations
- 10/4: Laplace transforms (forward and inverse)
- 10/9: Key properties; initial and final value theorems
- 10/11: Transfer functions v. 1
- 10/16:
**Fall break — no class** - 10/18: Connections between Fourier and Laplace; review for Quiz 2
- 10/23:
**Quiz 2**

- Linear systems
- 10/25: Solving differential equations; partial fraction expansions
- 10/30: Zero-state and zero-input responses
- 11/1: Transfer functions v. 2
- 11/6: Modes, poles and zeros; stability
- 11/8:
**Lab 2: Circuit system identification** - 11/13: Frequency response v. 2; review for Quiz 3
- 11/15:
**Quiz 3**

- Feedback
- 11/20: Block diagrams; closed-loop systems
- 11/22:
**Thanksgiving break — no class** - 11/27: Control design
- 11/29: P and PI regulators
- 12/4:
**Lab 3: Control of a DC motor** - 12/6: Review for final exam

- 12/13:
**Final exam**– 11:30-2:20–>

## Administrivia

**Textbook:**Chi-Tsong Chen,

*Signals and Systems*, Third Edition, Oxford University Press, 2004.

(Miscellaneous notes will also be posted on T-square.)**Workload and Grading:**

There will be approximately nine

homework sets, three in-class labs, two quizzes, and a comprehensive,

closed-book final exam. Grading is as follows:

Homework: 30%, Labs: 15%, Quizzes: 30%, Final Exam: 25%**Homework:**

The credit for the homework sets will be divided between programming assignments and theoretical exercises. MATLAB will be used for the programming assignments. Each of you is expected to turn in homework that is completely your own work, but you may discuss problems and solution approaches with others. Be sure to attempt each problem on your own before seeking help. Working homework is the best way to learn the material and do well in the class. Homework must be neat and well-organized or it may not be graded or may have points deducted. Be sure to put your name, the date, and the assignment number on the front page in the upper right corner or on a cover sheet.**In-class labs:**

As part of this course, three in-class labs will be conducted to make some

practical sense out of the theoretical developments in the class. The labs

will be based on the NI myDAQ board, and the boards will be provided for the

in-class labs. If you want more time or want to probe further, you can either

buy this board (available

here or use the devices in Van Leer E383 and E375 on Mondays and Fridays from 7:30 am to 8:00 pm.

The three lab topics will be:- Fourier and vibrating guitar strings
- Frequency response of filter circuits
- Feedback control of a DC motor
**Passing this class requires attendance in all three labs.**

**Looking for feedback:**This is the second semester this class

has been taught, so there may be some rough edges. We welcome any thoughts

you might have that could improve the course, both in content and structure.**Coordination with the other section:**Prof. Jennifer Michaels

is teaching

the “A” section of ECE3084 this semester. We intend to coordinate closely,

and will try to stay reasonably in sync. Homework due

dates, quiz dates, lab dates, etc. will vary because our sections are on

different days,

but we’ll try to stay in the same ballpark. You should consider us a team;

Prof. Michaels

students are welcome to ask me and my TA for help and vice-versa.**Office hours**:

Shortly before assignments are due,

I will post an announcement on Piazza describing when and

where I will be sure to be available for questions.

This will tend to change slightly from week to week,

so look for that announcement.

(Also, if you walk by my office and happen to see my

VL431 office door open,

you are welcome to pop in with questions about the class and/or life in general.)Of course you are always welcome

to e-mail me and we can set up a specific time to meet. Again, put “3084” in the subject line.**On-line discussions:**We will use

Piazza

to facilitate class discussions. We will try

to check Piazza at least once a day. You are welcome to post questions about anything

related to the course material, and also answer other student’s questions, as long as

you don’t “give away the answer” or post chunks of code that are more than a few lines.**T-Square**:

T-square

is the primary means of distributing information.

Please note that homework assignments and labs will be posted on T-Square and will not be handed out in class. The following information will also be found on T-Square as it becomes available: (1) homework solutions, (2) quiz solutions, (3) class grades, (4) this syllabus, and (5) miscellaneous handouts. Homework assignments will be the same for Sections A and B, but the quizzes and final will be different.**Major emergencies:**

If you have some sort of major life emergency – serious illness or injury,

death in the family, house burns down or is flooded, etc. – that seriously

impedes your progress in the class, please let me know as soon as possible

so we can work something out.

You will find professors can be quite reasonable if you keep us in the loop.

Please don’t disappear with no warning half way through,

making me think that you dropped the class, and then reappear out of

nowhere the week before finals asking what you can do to make things up.

(Yes, this has happened quite a bit, in both undergrad and grad classes.)**On things that distract:**

Please silence all cell phones and pagers

before entering class. If you forget to do so and receive

a call, please shut the noisemaking device down as quickly as possible,

and return the person’s call*after*class. (Of course, there

are reasonable

exceptions, i.e. if your wife is in the 9th month of her pregnancy and may

give birth at any moment or your

kid isn’t feeling well but he or she

went to school anyway and their school nurse

may need to call you, leave your

phone on vibrate, and answer it as quickly as possible and

immediately step out

of the room to handle the call.)**In general, please do not instant message, websurf, Facebook**.

(can I use it as a verb?),

e-mail,

play games, etc. during class

It can be quite distracting.

**Unless I say otherwise, the preferred position for laptops during**.

class is in your backpack**The Twitter exception:**

If

Prof. Lanterman says something particularly brilliant and clever during lecture,

you are allowed to

use your phone to Tweet it or post

it to Facebook.**Honor code:**

Adherence to the Georgia Tech Honor Code is expected and all suspected instances of academic misconduct will be reported to the Dean of Students. It is your responsibility to ask for clarification if collaboration guidelines, test-taking policies, etc. are not clear.