ECE 340: Discrete Time Signals and Systems
Lecture 20: The Transfer Function & System Realization
November 18, 2014
Lecturer: Majid Khabbazian
1. Zero-State Response of LTID Systems: The Transfer Function
Consider an an nth-order LTID system specied by t
ECE 340: Discrete Time Signals and Systems
Lecture 14: Z-transform
October 21, 2014
Lecturer: Majid Khabbazian
1. A Very Special Function for LTID Systems: The Exponential zk
The response y[k] of and LTID system to input f [k] = z k is
k
y[k] = h[k] z =
ECE 340: Discrete Time Signals and Systems
Lecture 11: Periodic Extension of Fourier Spectrum
October 9, 2014
Lecturer: Majid Khabbazian
1. Recap
We can represent any N0 -periodic signal f [k] as the following discrete-time Fourier series
(DTFS)
N0 1
Dr
ECE 340: Discrete Time Signals and Systems
Lecture 10: Discrete-Time Fourier Series (DTFS) Periodic Signals
October 7, 2013
Lecturer: Majid Khabbazian
1. Introduction
Previously, we showed that any discrete-time signal f [k] can be represented as a weigh
ECE 340: Discrete Time Signals and Systems
Lecture 9: Difference EquationsTotal Response, and System Stability
October 2, 2014
Lecturer: Majid Khabbazian
1. Total response of the system
So far, we learned how to nd the zero-input response, and, h[k], the
ECE 340: Discrete Time Signals and Systems
Lecture 8: Difference EquationsUnit Impulse Response
September 30, 2014
Lecturer: Majid Khabbazian
1. Unit impulse response Introduction
Question: An LTID system outputs zero if its input is zero. Why the zero-i
ECE 340: Discrete Time Signals and Systems
Lecture 6: Difference Equations
September 23, 2014
Lecturer: Majid Khabbazian
1. Difference Equations An special case
Solving an special case where an1 , . . . , a0 = 0
y[k + n] = bn f [k + n] + bn1 f [k + n 1]
ECE 340: Discrete Time Signals and Systems
Lecture 5: More on discrete-time signals and systems
September 18, 2014
Lecturer: Majid Khabbazian
1. Size of a Discrete-Time Signal
Size of a discrete-time signal f [k] is measured by its energy Ef dened by
|f
ECE 340: Discrete Time Signals and Systems
Lecture 16: Some Properties of the Z-Transform
October 30, 2014
Lecturer: Majid Khabbazian
1. Linearity
The Z-transform is a linear operation. That is, if
f1 [k] F1 [z] and
f2 [k] F2 [z]
then
a1 f1 [k] + a2 f2 [
ECE 340: Discrete Time Signals and Systems
Lecture 15: Z-transform
October 23, 2014
Lecturer: Majid Khabbazian
1. Recap: The Z-Transform
The Z-transform of f [k] is dened as
f [k]z k .
F [z] =
k=
The direct and inverse Z-transforms can be expressed as
F
ECE 340: Discrete Time Signals and Systems
Lecture 12: Discrete-Time Fourier Transrom (DTFT) Aperiodic Signals
October 14, 2014
Lecturer: Majid Khabbazian
We showed that periodic signals can be represented as a sum of exponentials.
Can we represent aperio
ECE 340: Discrete Time Signals and Systems
Lecture 22: Frequency Response From Pole-Zero Location
November 25, 2014
Lecturer: Majid Khabbazian
1. Frequency Response From Pole-Zero Location
Review:
(a) A complex number can be represented by a vector in th
ECE 340: Discrete Time Signals and Systems
Lecture 23: Solving Midterm Questions
December 2, 2014
Lecturer: Majid Khabbazian
a
1. cos(ak + b) is periodic if and only if 2 is rational. To nd the period, we can write
and q are integers with common factor of
ECE 340: Discrete Time Signals and Systems
Lecture 23: Basics of Digital Filters
November 27, 2014
Lecturer: Majid Khabbazian
1. Review
A digital lter is a digital system that transforms a sequence, applied at the input of the lter, by
changing its freque
ECE 340: Discrete Time Signals and Systems
Lecture 21: The Bilateral Z-transform + System response to Sinusoidal input
November 20, 2014
Lecturer: Majid Khabbazian
1. Introduction
The bilateral Z-transform denition:
f [k]z k
F [z] =
k=
The unilateral Z-
ECE 340: Discrete Time Signals and Systems
Lecture 19: Z-Transform Solution to Linear Difference Equations
November 13, 2014
Lecturer: Majid Khabbazian
1. Recap
Suppose m is a non-negative integer.
Left Shift (Advance)
f [k + m]u[k] z m F [z] z m f [0]
ECE 340: Discrete Time Signals and Systems
Lecture 18: Inverse Z-transform of rational Functions
November 6, 2014
Lecturer: Majid Khabbazian
1. More Examples
Example: Find the inverse Z-transform of
(a)
(b)
z(2z 2 11z+12)
(z1)(z2)3
2z(3z+17)
(z1)(z 2 6z+
ECE 340: Discrete Time Signals and Systems
Lecture 13: Nature of Fourier Spectra and DTFT Properties
October 16, 2014
Lecturer: Majid Khabbazian
1. Nature of Fourier Spectra
The Fourier spectra are continuous functions of
Fourier integral is basically
ECE 340: Discrete Time Signals and Systems
Lecture 17: Inverse of the Z-Transform
November 4, 2014
Lecturer: Majid Khabbazian
1. Introduction
Many of the transforms F [z] of practical interest are rational functions, that is of the form
where P and Q are
ECE 340: Discrete Time Signals and Systems
Lecture 2: Introduction to Discrete-Time Signals: Part 2
September 9, 2014
Lecturer: Majid Khabbazian
1. Periodic signals
Denition 1 (N0 -periodic, where N0 is a positive integer). A discrete signal f [k] is said
ECE 340: Discrete Time Signals and Systems
Lecture 1: Introduction to Discrete-Time Signals: Part 1
September 4, 2014
Lecturer: Majid Khabbazian
1. Brief Introduction
There is a signicant similarity between the results seen in continuous-time case with r
ECE 340: Discrete Time Signals and Systems
Lecture 2: Introduction to Discrete-Time Signals: Part 2 Examples
September 9, 2014
Lecturer: Majid Khabbazian
1. Example: A discrete-time amplier uses a sampling interval T = 25s. What is the highest frequency o
Assignment 9 (Last Assignment :-)
Name & Student Number:
ECE 340
Discrete-Time Signals and Systems
Fall 2014
Due date: Nov. 28, 2014 @ 3:30 pm
Marks
Question
Q1
Q2
Q3
Q4
Q5
TOTAL
Mark
6
4
3
5
3
21
1 of 2
Your Mark
Assignment 9 (Last Assignment :-)
Q1 cfw_
Assignment 8
Name & Student Number:
ECE 340
Discrete-Time Signals and Systems
Fall 2014
Due date: Nov. 20, 2014 @ 3:30 pm
Marks
Question
Q1
Q2
Q3
Q4
TOTAL
Mark
4
5
5
5
19
1 of 2
Your Mark
Assignment 8
Q1 cfw_4 marksFind the rst three terms of the causal s
Assignment 6
Name & Student Number:
ECE 340
Discrete-Time Signals and Systems
Fall 2014
Due date: Nov. 6, 2014 @ 3:30 pm
Marks
Question
Q1
Q2
Q3
Q4
Q5
Q6
TOTAL
Mark
5
5
5
5
5
3
28
1 of 2
Your Mark
Assignment 6
Q1 cfw_5 marksFind the discrete-time Fourier
Assignment 7
Name & Student Number:
ECE 340
Discrete-Time Signals and Systems
Fall 2014
Due date: Nov. 13, 2014 @ 3:30 pm
Marks
Question
Q1
Q2
Q3
Q4
TOTAL
Mark
4
4
12
10
30
1 of 2
Your Mark
Assignment 7
Q1 cfw_4 marksUsing the denition of Z-transform, sho
Assignment 2
Name & Student Number:
ECE 340
Discrete-Time Signals and Systems
Fall 2014
Due date: Oct. 2, 2014 @ 3:30 pm
Marks
Question
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
TOTAL
Mark
4
3
4
4
5
4
4
3
31
1 of 2
Your Mark
Assignment 2
Q1 cfw_4 marksIf f [k] = (0.8)k u[k
Assignment 3
Name & Student Number:
ECE 340
Discrete-Time Signals and Systems
Fall 2014
Due date: Oct. 9, 2014 @ 3:30 pm
Marks
Question
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
TOTAL
Mark
3
6
2
6
3
3
4
6
33
1 of 3
Your Mark
Assignment 3
Q1 cfw_3 marksShow that a necessary
Assignment 4
Name & Student Number:
ECE 340
Discrete-Time Signals and Systems
Fall 2014
Due date: Oct. 16, 2014 @ 3:30 pm
Marks
Question
Q1
Q2
Q3
Q4
Q5
TOTAL
Mark
6
3
4
3
6
22
1 of 2
Your Mark
Assignment 4
Note: For questions Q2, Q3, and Q4 you can use th