### Module Specification

 The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
 Title Signals and Systems Code ELEC270 Coordinator Dr W Al-Nuaimy Electrical Engineering and Electronics Wax@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2021-22 Level 5 FHEQ First Semester 15

### Aims

To introduce the student to the fundamentals of the analysis of continuous- and discrete-time signals and systems. To equip the student with the mathematical tools that would allow them to design and/or analyse a linear time-invariant system, e.g. a filter. To present the concepts involved with signals and systems. Namely: Signal Classification, Representation and Analysis Fourier Series Fourier Transform Laplace Transform Linear Time-invariant (LTI) Systems and Filters Discrete-time Fourier Series Discrete-time Fourier Transform z-Transform

### Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

MATH191 MATHEMATICS I FOR ELECTRICAL ENGINEERS; MATH192 MATHEMATICS II FOR ELECTRICAL ENGINEERS

### Learning Outcomes

(LO1) An understanding of the use of Fourier Series to represent periodic continuous-time signals.

(LO2) An understanding of the use of the Fourier Transform to represent finite energy signals.

(LO3) An understanding of the Laplace Transform, its properties and its use in circuit and system analysis.

(LO4) An understanding of the use of Discrete-time Fourier Series to represent periodic discrete-time signals.

(LO5) An understanding of the use of the Discrete-time Fourier Transform.

(LO6) An understanding of the z-Transform, its properties and its use for discrete-time signals and systems.

(LO7) An understanding of the relationship between time and frequency domains.

(LO8) An understanding of Linear Time Invariant Systems, and filters, both in the continuous- and discrete-time domains.

(LO9) An appreciation of the relationship between the system function and the frequency response.

(LO10) The ability to deal with real physcial signals and analyse, synthesise and otherwise manipulate them using available laboratory equipment.

(LO11) An appreciation of the relationship between the syst em function and the frequency response.

(S1) On successful completion of the module, students should be able to show experience and enhancement of the following key skills: Independent learning Problem solving and design skills

(S2) After completion of the module, the student should have: the ability to analyse continuous- and discrete-time signals and to design and analyse simple linear continuous and discrete systems

### Syllabus

Continuous-time signals & systems
Introduction to signals & systems: Signal Classification, Representation and Analysis; Signals classification as periodic/aperiodic; causal/non-causal; deterministic/random; finite energy/finite power; analogue and digital signals.

Fourier Series: Time and frequency domain description of signals; Trigonometric and complex exponential Fourier series; Symmetry and time-shifting properties and Amplitude and power spectra.

Fourier Transform: Fourier transform and inverse transform; Spectral density; Convolution theory; Fast Fourier transform and Examples.

Laplace Transform: Laplace transform and inverse Laplace transform; Properties including linearity, time-diffentiation and integration; Generalisation of the Fourier transform.

Linear Time-invariant (LTI) Systems and Filters:
Definition of an LTI system; convolution integral; impulse response; step response; frequency response; transfer function; use of Fourier transform and Laplace transform, stability, poles and zeros and Filters.

Discrete-time signals & systems:
Introduction; Overview of Discrete-time Signals & Systems; Discrete Time Fourier Series; Discrete Time Fourier Transform; Z-transform; Discrete-time Linear Time Invariant (DT-LTI) Systems.

### Teaching and Learning Strategies

Due to Covid-19, one or more of the following delivery methods will be implemented based on the current local conditions. and safety guidelines.

(a) Hybrid delivery, with social distancing on Campus

Teaching Method 1 - On-line asynchronous lectures
Description: Lectures to explain the material
Attendance Recorded: No
Notes: On average one per week

Teaching Method 2 - Synchronous face to face tutorials
Description: Tutorials on the Assignments and Problem Sheets
Attendance Recorded: Yes
Notes: On average one per week

(b) Fully online delivery and assessment

Teaching Method 1 - On-line asynchronous lectures
Description: Lectures to explain the material
Attendance Recorded: No
Notes: On average one per week

Teaching Method 2 - On-line synchronous tutorials
Description: Tutorials on the Assignments and Problem Sheets
Attendance Recorded: Yes Notes: On average one per week

(c) Standard on-campus delivery with minimal social distancing

Teaching Method 1 - Lecture
Description: Lectures to explain the material
Attendance Recorded: Yes
Notes: On average one per week

Teaching Method 2 - Tutorial
Description: Tutorials on the Assignments and Problem Sheets
Attendance Recorded: Yes
Notes: On average one per week

### Teaching Schedule

 Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL Study Hours 12 12 7 6 8 45 Timetable (if known) Private Study 105 TOTAL HOURS 150

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Assessment 3 There is a resit opportunity. Non-standard penalty applies for late submission - N/A This is an anonymous assessment. Assessment Schedule (When) :Semester 1 examination period  2 hours    50
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Assessment 1 There is a resit opportunity. Standard UoL penalty applies for late submission. This is not an anonymous assessment. Assessment Schedule (When) :As scheduled - Semester 1  7 hour lab session,     10
Class Tests x 6 There are no resit opportunities. Non-standard penalty applies for late submission - Hard online deadline. This is an anonymous assessment. Assessment Schedule (When) : As sched  1 hour    40

### Reading List

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.