EE 20N: STRUCTURE AND INTERPRETATION OF SIGNALS AND
SYSTEMS
Department:
Electrical Engineering and Computer Sciences
Instructor:
Dr. Babak Ayazifar (EECS Faculty)
Credit Units:
Prerequisites:
4
Math 1B (first-year calculus, second course)
Course Structure:
 Lecture hours per week (Lec):
 Discussion (recitation) section
hours per week (D):
 Instructor office hours, focused on groupbased problem solving (OH):
 Laboratory hours per week (Lab):
3
1 (not mandatory)
2 (not mandatory)
3
Course Components:
 Problem Sets/Homework (HW)
 Laboratory Exercises (Lab)
 Pop quizzes (Q)
 Exams (E)
Textbooks:
 Required:
o E. A. Lee and P. Varaiya, Structure and Interpretation of Signals
and Systems, Addison-Wesley
 Course covers a superset of
 Appendix A (sets and functions)
 Appendix B (complex numbers)
 Chapter 1 (Signals and Systems)
 Chapter 2 (Defining Signals and Systems)
 Chapter 7 (Frequency Domain)
 Chapter 8 (Frequency Response)
 Chapter 9 (Filtering)
 Chapter 10 (The Four Fourier Transforms)
 Chapter 11 (Sampling and Reconstruction)
o LabVIEW exercises developed for the course, issued to students
throughout the semester (in revision).
 Recommended:
o A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and
Systems, Prentice-Hall, 1997.
o H. P. Hsu, Schaum’s Outline of Signals and Systems, McGraw-Hill,
1995.
RELATIONSHIP TO ABET PROGRAM OUTCOMES:
Students who complete this course successfully meet the following ABET
program outcomes: (a), (b), (c), (e), (g), (i), (k).
EE 20N requires students to apply a fundamental knowledge of mathematics,
science and engineering to not only solve electrical and computer engineering
problems, but also appreciate the multidisciplinary reach of the topics and
techniques emphasized in the course.
Students learn modern skills, techniques and engineering tools. They cultivate
the intuition to perform back-of-the-envelope and design-oriented analysis. They
learn to model and simulate signals and systems, and to interpret data from their
computational work.
Problem sets and exams are designed to probe a thorough understanding of
fundamental concepts and to de-emphasize rote algebraic manipulation.
Exam problems insist on refined and to-the-point responses; limited space is
allocated for each problem to encourage students to think more clearly and
logically, and to articulate their responses efficiently and without clutter. The
various components of the course encourage students to think graphically and
draw, before they reach for mathematical formulae.
Lectures, discussion sections, labs, and instructor’s office hours promote group
work by engaging the students in a collaborative learning environment where
they divide into groups of 3-5 students and discuss the solutions to the various
problems posed to them. In discussion sections and office hours, students are
asked to present their solutions to their peers on the board, to guide discussion
among their peers by asking each other questions and assisting each other
toward solutions.
Recognizing that team work is an integral part of engineering practice, the
homework policy encourages collaborative groups of up to five students.
COURSE LEARNING OBJECTIVES AND OUTCOMES:
This course provides students with a working knowledge of the basic concepts of
signals and systems in both continuous-time and discrete-time. Upon successful
completion, a student should:

Know the essentials of sets and set operations—in particular, the
properties of the sets of real numbers, integers, and complex numbers.
Coverage: Lec, D, HW, Q, E, OH, Lab (for complex numbers)
Student Success: Excellent

Know the essentials of symbolic logic, and be able to carry out basic proof
methods, such as “proof by contradiction,” “proof by counter-example,”
“proof by induction,” etc.
Coverage: Lec, D, HW, Q, E, OH
Student Success: Fair

Know the algebra of complex numbers and functions, including their
Cartesian and polar representations, and their magnitudes and phases.
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Excellent

Recognize that signals and systems are functions that map elements in a
respective domain to elements in a corresponding co-domain.
Coverage: Lec, D, HW, Q, E, OH
Student Success: Excellent

Recognize the various categories of signals (continuous-time, discretetime, analog, and digital) as well as systems, based on the nature of the
domains and co-domains that characterize their functional
representations.
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Excellent

Graph mathematical descriptions of discrete-time and continuous-time
signals (including magnitude and phase plots of complex-valued
functions), and write mathematical descriptions of graphed functions.
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Excellent

Classify systems based on their properties: in particular, understand and
exploit the implications of linearity, time-invariance, causality, and
memory.
Coverage: Lec, D, HW, Q, E, OH
Student Success: Very Good

Understand the combined implications of linearity and time invariance in
the time domain—the time-domain properties of linear, time-invariant (LTI)
systems. In particular,
o represent an LTI system by an impulse response; and
o determine the response of the LTI system to an arbitrary input
signal using convolution.
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Very Good

Understand the combined implications of linearity and time invariance in
the frequency domain—the frequency-domain properties of linear, timeinvariant (LTI) systems. In particular,
o represent the response of an LTI system to a complex exponential
and understand that complex exponentials are eigenfunctions of
LTI systems;
o represent an LTI systems by its frequency response function
(magnitude and phase).
o determine the input-output behavior of an LTI system entirely in the
frequency domain.
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Excellent

Understand an LTI system’s frequency response in terms of both
magnitude and phase, and recognize design principles behind basic filters
such as low-pass, band-pass, high-pass, comb, notch, and anti-notch.
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Very Good

Know how to decompose a signal in terms of a linear combination of
impulses in the time domain.
Coverage: Lec, D, HW, Q, E, OH
Student Success: Excellent

Know how to decompose a signal in terms of complex exponentials in the
frequency domain:
o Periodic Signals: determine Fourier series coefficients for both
discrete-time and continuous-time periodic signals, and understand
the implications of what the coefficients mean;
o Aperiodic Signals: determine Fourier transforms for both
continuous-time and discrete-time signals (or impulse-response
functions), and understand how to interpret and plot Fourier
transform magnitude and phase responses.
o Understand the impulsive nature of the Fourier transforms of
periodic signals.
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Very Good

Understand the various properties of transforms—including time-shift,
modulation (frequency shift), duality, symmetry and anti-symmetry—and
exploit them to analyze and design signals and systems.
Coverage: Lec, D, HW, Q, E, OH
Student Success: Good

Understand the relationships among various representations of LTI
systems—linear constant-coefficient difference or differential equation,
frequency response, and impulse response—and to infer one
representation from another (e.g., determine the impulse response from
the difference equation, etc.)
Coverage: Lec, D, HW, Q, E, OH
Student Success: Very Good

Understand the properties, as well the analysis and design implications, of
interconnections of LTI systems—parallel, series (cascade), and
feedback—in the time and frequency domains.
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Excellent

Understand the sampling theorem, how to derive it from first principles and
basic properties of the continuous-time Fourier transform, and how to use
to understand aliasing phenomena in the real-world (e.g., the carriage
wheel effect).
Coverage: Lec, D, HW, Q, E, OH, Lab
Student Success: Fair

Use computer tools, such as LabVIEW, to simulate, analyze, and design
discrete-time and continuous-time signals and systems.
Coverage: Lab
Student Success: Very Good
TOPICS COVERED:

Mathematical Foundations – Sets and functions; Fundamentals of
mathematical logic; Complex algebra (including complex-valued
functions); Basic linear algebra (matrix-vector manipulations of 2x2
matrices; Vector-space concepts (e.g., basis, dimension, inner products,
orthogonal basis expansions).

Signals – Signals as functions: continuous time, discrete time; Signals as
vectors in an appropriately-defined vector space having an appropriatelydefined inner product; Orthogonality of signals; Two-dimensional space
continuum; Discrete-space: discrete time and continuous space, discrete
time and mixed space, discrete time and space, discrete events, discrete
events and discrete time; Sequences.

Sinusoids – Periodic signals, sinusoids-phase and amplitude, complex
numbers, complex signals, complex exponentials; Phasors, amplitude
modulation, frequency modulation.

Spectrum – Summing sinusoids, approximating periodic signals,
harmonics and musical sounds, beat notes, two-dimensional sinusoids;
Approximating images.

Sampling – Analog-to-digital conversion, aliasing, downsampling, digitalto-analog conversion, upsampling, oversampling CD players.

Systems – Filters, Running average filter, Two-dimensional running
average filter, FIR filters; IIR filters; Linearity; Time invariance; Causality;
Memory; Impulse response; Convolution. Difference-equation
representations of LTI systems.

Frequency Response and Filtering – Sinusoidal input, complex
sinusoidal input, transfer function; Filtering audio signals, blurring and
sharpening images.

Fourier Series and Transforms – Fourier series using vector-space
concepts; Signals viewed as vectors; Harmonically-related sinusoids and
complex exponentials are viewed as orthogonal vectors in an
appropriately-defined vector space; Discrete Fourier series (DFS/DFT);
Continuous-time Fourier series (FS); Discrete-time Fourier transform
(DTFT); Continuous-time Fourier transform (CTFT).

Spectrum Analysis – Spectra of periodic and aperiodic signals; Time and
frequency sampling; Amplitude modulation; Spectrograms.

Interconnections of Systems: Parallel, Cascade, and Feedback;
implications of interconnected LTI systems for their time-domain and
frequency-domain behaviors.

Miscellaneous Topics – Hard limiting; Edge detection; Fractals and
chaos; Noise in musical sounds and images.
Prepared by:
Babak Ayazifar
Date:
February 2009