This course serves to introduce students to the input-output mode of thinking. Students will be taught how to translate the everyday notions of cause and effect into input-output models. They will be required to study, understand and use a set of mathematical tools for describing and analyzing inputs and outputs and the relationships between them. They will study the nature of systems and learn techniques for analyzing and designing them to meet given performance criteria.
The description and use of mathematical tools required to analyze and design systems forms the bulk of the presentation in this course but by appealing to practical examples wherever possible students should never be allowed to lose sight of the real-world application of these tools.
In the presentation of this course and particularly in the tutorials, MATLAB will be used as an omnipresent anchor so that on completion all students should be proficient in its use. The learning experience is enhanced with computer-based exercises and assignments. The assignment will include: (1) take home problem solving questions design to test student understanding of the theory; and (2) a report in the form of an IEEE paper structure on a survey of the state-of-the-art in signal and systems or system engineering. The intent is to expose the student to high level technical publications.
1. Continuous-Time Signals and Systems
Continuous-Time Elementary Signals: The Unit Step, the Unit Impulse, the Unit Ramp, Sinusoidal Signal
Signal Transformations: Continuity, Piece-wise continuity; Time shifting, time scaling, time reversal; Convolution; Convolution and Impulse Response
Introduction to Systems: is a system? Modelling of Physical Systems, Linear Differential Equations, I/O State Space; Properties of Systems (I/O, Linearity, TI,Causality); Testing for System Properties
Frequency Domain Representation of Signals and Systems: The Fourier Series; Trigonometric Form; Complex Exponential Form; Representation of Periodic Signals; Transform
Transform Domain Representation of Systems: Laplace Transfer; System Transfer Function; Block Diagrams; Signal Flow Graphs
Time Domain Analysis of Systems: System Response; Zero Input Response; Zero State Response; Input-Output Relationships for LTI Systems; and the Impulse Response; The Routh-Hurwitz Criterion; Step Response Analysis; Frequency Response; Space Analysis
2. DISCRETE-TIME SIGNALS AND SYSTEMS
Mathematical Representation of Discrete-Time Signals: Difference Equations; z-Transform; Inverse Transform; Division Z-Transform Inversion; Fraction Expansion; Equations
Frequency Domain Representation of Discrete-Time Signals: Discrete-Time Fourier Transforms; Discrete-Time Fourier Series; Discrete Fourier Transforms; Comparison of Fourier Transforms
Time Domain Representation of Discrete-Time Systems: System Classification; Discrete Time Systems; Discrete Time Convolution; of Discrete-Time Convolution; of Discrete-time Systems
Transform Domain Representation of Discrete-Time Systems; Discrete-Time Systems; Stability of Discrete-Time Systems; Time Steady State Response
Filter Design: Analog Filters; Digital Filters (FIR and IIR Filters)
One 2-hour theory final exam paper – 60%
Mid Semester exam - 20%
Assignments – 20%
On completion of this course, students should be able to:
Text book: “Signals and Systems: With MATLAB Computing and Simulink Modeling’- by Steven Karris: 4th Edition; Orchard Publications, 2008
Supplemental Reading: Signals, and Systems, Schaum’s Outline Series Hsu, HweiP, McGraw-Hill, 1997 (3rd Ed)
Internet Resources:
Signals, and Systems, Schaum’s Outline Series (PDF)
MIT LECTURE NOTES PROBLEM SETS AND SOLUTIONS FOR SIGNALS AND SYSTEMS
Our 7 faculties and 12 professional schools offer more than 200 programmes to some 18,000 graduate, undergraduate and continuing studies students.
The UWI, Mona ranks first in Jamaica among accredited tertiary-level programmes. In 2012, the University was again one of Jamaica’s Top 100 Employers.
