EE120_F'08 Outcomes List – Babak Ayazifar
COURSE LEARNING OBJECTIVES AND OUTCOMES:
This course trains students for an intermediate level of fluency with signals and systems in both
continuous time and discrete time, in preparation for more advanced subjects in digital signal
processing (including audio, image and video processing), communication theory, and system
theory, control, and robotics.
Upon successful completion, a student should:

Be able to classify systems based on their properties: in particular, to understand and
exploit the implications of linearity, time-invariance, causality, memory, and boundedinput, bounded-out (BIBO) stability.

Know the principles of vector spaces, including how to relate the concepts of basis,
dimension, inner product, and norm to signals.

Learn to treat signals as vectors in a vector space and ascribe geometry to that space by
defining an appropriate inner product—in both discrete-time and continuous-time, and
for both periodic and aperiodic signals.

Know how to analyze, design, approximate, and manipulate signals using vector-space
concepts.

Determine Fourier transforms for continuous-time and discrete-time signals (or impulseresponse functions), and understand how to interpret and plot Fourier transform
magnitude and phase functions.

Understand the sampling theorem and how it links continuous-time signals to discretetime signals. In particular, know how to derive the sampling theorem from first
principles—from the basic properties of the Fourier transform; how the spectrum of a
sampled signal relates to the spectrum of the original signal; how to use the sampling
theorem to understand aliasing phenomena in the real-world (e.g., the carriage wheel
effect), and how to reduce or prevent aliasing; and how to perform discrete-time
processing of continuous-time signals, and vice versa, using C/D and D/C converters.

Understand the need to define two new transforms—the Laplace and Z transforms—to
treat a class of signals broader than what the Fourier transform can handle.

Understand the combined implications of linearity and time invariance in the Laplace and
Z transform domains. In particular, know how to represent the response of an LTI
system to a more general form of complex exponential—est in continuous time or zn in
discrete-time—and understand that complex exponentials are eigenfunctions of LTI
systems; use the Laplace transform to determine the transfer function of a continuoustime LTI system; solve for a response given the input, system description and initial
conditions; and answer questions related to BIBO stability, including the central role of
the -axis in the transform-domain representations of continuous-time signals and
systems; use the Z transform to determine the transfer function of a discrete-time LTI
system; solve for a response given the input, system description and initial conditions;
and answer questions related to BIBO stability, including the central role of the unit
circle in the transform-domain representations of discrete-time signals and systems;
represent an LTI system by its transfer function; determine the input-output behavior of
an LTI system entirely in the transform domain, using relationships between time-domain
and the frequency-domain (e.g., convolution in the time domain corresponds to
multiplication in the frequency domain); understand the conditions under which the
transfer function of a system (or the Laplace or Z transform of a signal) is rational, and
know that a continuous-time LTI system with a rational transfer function can be
represented by a linear, constant-coefficient differential equation; and a discrete-time LTI
system with a rational transfer function can be represented by a linear, constantcoefficient difference equation.

Understand the relationships among the various representations of LTI systems—linear
constant-coefficient difference or differential equation, frequency response, transfer
function, and impulse response—and infer one representation from another (e.g.,
determine the impulse response from the difference equation, etc.).

Understand the conditions for a time-domain function to have a Fourier transform, and
know how to relate the Fourier transform to its Laplace or Z transform.

Understand the various properties of the four Fourier transforms, the Laplace transform,
and the Z transform—including time-shift, modulation (frequency shift), duality,
symmetry and anti-symmetry—and exploit them to analyze and design signals and
systems.

Understand the properties, as well the analysis and design implications, of
interconnections of LTI systems—parallel, series (cascade), and feedback—in the time
and transform domains.

Know how to derive and exploit basic concepts in communication theory, including
amplitude modulation and frequency modulation.

Understand how to use the unilateral Laplace or Z transform to decompose the response
of an LTI system into a zero-state component and a zero-input component, and solve
linear, constant-coefficient differential or difference equations, with possibly non-zero
initial conditions.

Develop reasonably-accurate mathematical models for physical systems, find LTI
approximations to the models, produce block-diagram implementations of the
mathematical models, and analyze the block diagram realizations with a view toward
designing more complex systems or more sophisticated models.

Learn to develop and analyze state-space models of linear and nonlinear systems. This
includes drawing qualitative plots of state trajectories; determining internal stability
including the stability of equilibrium points; determining the modes of LTI systems,
especially second-order systems, by performing eigenanalysis of the state transition
matrix; and developing an aptitude for modeling a multidisciplinary array of systems in
state-space form.