ECTE203 Lectures of Part B
Lecture
Topic
L7
Discrete signals and sampling theorem
L8
Convolution in discrete-time domain
L9
The z-transform
L10
Frequency response of a discrete LTI
system
L11
FIR and IIR filters
L12
Class Test 2
L13
Revision
2
Lecture 9 -

ECTE203
Lecture 4
Frequency Response of
Continuous-Time Systems
Lecture 4, Spr16
2003, JH McClellan & RW Schafer. Modified
by C Ritz, 2009-2015, J Donley, 2016
1
License Info for SPFirst Slides
Most of This work released under a Creative Commons
License

ECTE203: Signals and Systems
Tutorial 6: Discrete signals and sampling theorem
Solution
1. [P-4.2] Sampling a sinusoidal signal
. The signal
Consider a continuous-time signal
a discrete-time signal
that is written as
is sampled at a rate of
For each of th

ECTE203: Signals and Systems
Tutorial 7: Convolution in the discrete-time domain
1. [P-5.9] Definition of Linearity, Time-Invariance, and Causality
For each of the following systems, determine whether the system is (i) linear, (ii) time-invariant, and (ii

ECTE203: Signals and Systems
Tutorial 9: Frequency response of a discrete LTI system
1. [P-6.7] Finding inverse Discrete-time Fourier Transform
For each of the following frequency responses
, determine the impulse response
(a)
(b)
(c)
2. [P-6.8] Analysing

ECTE203: Signals and Systems
Tutorial 10: FIR and IIR filters
1. Direct Form and Transpose Form
Draw the direct form and the transposed form for the FIR filter given by
y[n] 2 x[n] 3x[n 1] x[n 2]
2. Direct Form I and Direct Form II
a) Draw the direct form

ECTE203: Signals and Systems
Tutorial 7: Convolution in the discrete-time domain
1. [P-5.9] Definition of Linearity, Time-Invariance, and Causality
For each of the following systems, determine whether the system is (i) linear, (ii) time-invariant, and (ii

ECTE203: Signals and Systems
Tutorial 8: The z-transform
1. Finding z-transform
Using the properties of the z-transform and the table of common z-transform pairs, find the z-transform of
the following signals.
(a)
(b)
x2[n] cos(0n)u[n]
(c)
(d)
2. [P-8.11

ECTE203: Signals and Systems
Tutorial 6: Discrete signals and sampling theorem
1. [P-4.2] Sampling a sinusoidal signal
Consider a continuous-time signal
discrete-time signal
that is written as
. The signal
is sampled at a rate of
For each of the following

Formulae for Part B
Sampling and aliasing
,
Nyquist rate
=
Folding frequency
=
,
,
,
,
,
Aliasing
Discrete-time Convolution
Definition:
Commutative:
Distributive:
Associative:
With unit impulse:
Table of z-transform properties
Property name
Time-Domain
z-

ECTE203 Lectures of Part B
Lecture
Topic
L7
Discrete signals and sampling theorem
L8
Convolution in discrete-time domain
L9
The z-transform
L10
Frequency response of a discrete-time
LTI system
L11
FIR and IIR filters
L12
Class Test 2
L13
Revision
2
Lectur

ECTE203 Lectures of Part B
Lecture
Topic
L7
Discrete signals and sampling theorem
L8
Convolution in discrete-time domain
L9
The z-transform
L10
Frequency response of a discrete-time
LTI system
L11
FIR and IIR filters
L12
Class Test 2
L13
Revision
2
Introd

ECTE203 Lectures of Part B
Lecture
Topic
L7
Discrete signals and sampling theorem
L8
Convolution in discrete-time domain
L9
The z-transform
L10
Frequency response of a discrete LTI
system
L11
FIR and IIR filters
L12
Class Test 2
L13
Revision
2
Lecture 8 -

Overview of Part B
In Part A (Weeks 1-6), we have learnt techniques to
analyze continuous-time signals/systems.
In Part B (Weeks 7-12), we will focus on techniques
to analyze discrete-time signals/systems.
Key topics in Part B:
sampling and aliasing

ECTE203
Lecture 5
Introduction to the Fourier
Transform
Lecture 5, Spr16
2003, JH McClellan & RW Schafer. Modified
by C Ritz, 2009-2015, J Donley, 2016
1
License Info for SPFirst Slides
Most of This work released under a Creative Commons
License with th