# EEEN3003J Signals and Systems

Restriction: Beijing-based students only.

This course introduces the mathematical tools needed to analyse signals and the systems that process those signals.

The course starts with a definition of linear time-invariant (LTI) systems, defines one-dimensional (1D) signals as functions of time, and introduces the concept of periodic signals as elements of a vector space. Using these ideas the Fourier series (both the trigonometric and complex exponential forms) for such periodic signals is motivated and the relevant formulae presented.

The course then moves on to nonperiodic signals and the Fourier Transform. In this section the fundamental LTI theory is covered, including the Dirac delta impulse and the convolution integral. A number of classical ordinary differential problems are covered in detail, as is the concept of the continuous frequency spectrum e.g. AM modulation is explained, and the underlying concept of phasors from EEEN2001J is finally given firm justification.

The frequency domain concept is then extended to include signals which may have growth of exponential order using the Laplace transform. This is then applied to the analysis of systems which lead to ordinary differential equations with constant coefficients. The concept of the transfer function is introduced as the Laplace transform of the impulse response, and the distinction between forced, free, transient and steady-state system responses is explained.

Finally, feedback control systems are briefly introduced with some common applications of this theory explained through examples.

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Curricular information is subject to change

Learning Outcomes:

On successful completion of this module students should understand the basic concepts mentioned in the above description, including, but not limited to, the ability to;

- find the Fourier series of simple 1D periodic signals and infer certain properties of the Fourier coefficients from notable properties of the original signal;
- find the Fourier transform of simple 1D nonperiodic signals;
- understand and apply several properties of the Fourier transform;
- use Fourier theory to analyse LTI systems and solve simple linear differential equations;
- explain and apply the concept of convolution;
- explain the need for the Laplace transform;
- obtain transfer functions for linear circuits and systems,
- apply Laplace transform techniques to reduce systems described by ordinary differential equations to systems described by algebraic equations;
- solve such systems for a given input using inverse Laplace techniques;
- implement a simple feedback control system.

Student Effort Hours:
Student Effort Type Hours
Lectures

36

Laboratories

20

Autonomous Student Learning

60

Total

116

Approaches to Teaching and Learning:
Lectures where material is explained coupled with Labs where the students see first had the principles.

Requirements, Exclusions and Recommendations
Learning Requirements:

EEEN2001J OR Electronic Circuits module covering linear dynamic circuits, phasor analysis and amplifiers.

Mathematics modules on Linear Algebra and Calculus (covering matrices, eigenvalues/eigenvectors, differentiation, integration, linear differential equations)

Module Requisites and Incompatibles
:
-

This module is delivered overseas and is not available to students based at the UCD Belfield or UCD Blackrock campuses

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Report(s): 3 labs throughout the trimester Week 4, Week 8, Week 12 Alternative linear conversion grade scale 40% No

30

No
Exam (In-person): End-term exam End of trimester
Duration:
2 hr(s)
Alternative linear conversion grade scale 40% Yes

70

Yes

Carry forward of passed components
Yes

Remediation Type Remediation Timing
In-Module Resit Prior to relevant Programme Exam Board