ECE 4270 - Summer 2004 Homework Assignment #6
Assigned: June-16-2004 Due Date: June-23-2004
General Note:
Homework is due at class time on the Due Date; no late homework will be accepted. Make a COVER PAGE for your homework, including your name and GT nu
ECE 4270 - Summer 2004
Homework Assignment #4
Assigned: June-4-2004
Due Date: June-11-2004
General Note:
Homework is due at class time on the Due Date; no late homework will be accepted.
Make a COVER PAGE for your homework, including your name and GT numb
ECE 4270 - Summer 2004 Homework Assignment #7
Assigned: June-23-2004 Due Date: June-30-2004
General Note:
Homework is due at class time on the "Due Date"; no late homework will be accepted. Make a COVER PAGE for your homework, including your name and GT
ECE 4270 - Summer 2004 Homework Assignment #8
Assigned: June-30-2004 Due Date: July-14-2004
General Note:
Homework is due at class time on the "Due Date"; no late homework will be accepted. Make a COVER PAGE for your homework, including your name and GT
ECE 4270 - Summer 2004 Homework Assignment #9
Assigned: July-15-2004 Due Date: July-21-2004
General Note:
Homework is due at class time on the "Due Date"; no late homework will be accepted. Make a COVER PAGE for your homework, including your name and GT
Overview of Lectures 5 and 6
ECE4270
Fundamentals of DSP
Lectures 5, 6
Symmetry properties of the DTFT
The time-domain convolution theorem
Examples of usage of the DTFT
The Discrete-Time Fourier Transform
and
Random Processes
Random process
Probabili
ECE 4270
Fundamentals of Digital Signal Processing
Spectrum Analysis of Analog Signals Using
the Discrete Fourier Transform
Lecture 23:
Discrete Spectrum Analysis
School of Electrical and Computer Engineering
Georgia Institute of Technology
Summer 2004
Su
Overview of Lecture 1
ECE4270
Fundamentals of DSP
Lecture 1
Introduction & Overview
What is DSP?
Discrete-time signals
Examples
Discrete-time systems
Examples
Properties
School of Electrical and Computer
Engineering
Testing for properties
Linear t
ECE 4270 - Summer 2004
Homework Assignment #5
Assigned: June-10-2004
Due Date: June-16-2004
General Note:
Homework is due at class time on the Due Date; no late homework will be accepted.
Make a COVER PAGE for your homework, including your name and GT num
ECE 4270 - Summer 2004 Homework Assignment #1
Assigned: May-12-2004 Due Date: May-19-2004
General Note:
Homework is due at class time on the "Due Date"; no late homework will be accepted. Make a COVER PAGE for your homework, including your name and GT nu
Pop Quiz #2 (20 min.)
2
1
y[n 1] y[n 2] + x[n]
A causal LTI system is defined by the following difference equation y[ n] =
2
4
a)
Find H ( z ) , the system function;
b)
Find h[n] , the corresponding impulse response;
c)
Find the system output yu[n], for n
Problem 1 (30 points)
Signals x[n] and y[n] below form an input-output pair of a causal LTI system.
1
x[n]
n=0
1
-1
a)
b)
c)
1
y[n]
n
2
1
n=0
-2
(10 pts) Find the impulse response h[n] of the LTI system;
(10 pts) Find the frequency response of the system;
ECE-4270 Quiz #2
June 30, 2004
Prof. B.H. Juang
Student Name: _
Problem 1 (15 pts. ea., 30 pts total, c) is bonus)
a)
0
0
2
Fcfw_cos(n / 2)
= (
k
2
+ 2k ) + ( +
s = 3 0
2
x c (t )
+ 2k )
H 1 ( e j )
C/D
s = 4 0
4
cos(n / 2)
H 1 (e )
0
2
2
2
2
H 2 (e j
ECE4270, Oeteber 20, 2000: Qais #2 ' 2
Preblern 1: (30%)
A causal LTI system has system funetien
_. I -
1.28:3-2 2 e- - . 1'
(a) Determine A and B in the partial fraetien eapansien ef H(s) and frem it determine the
impulse respense Simplify year answe
ECE 4270 - Summer 2004 Homework Assignment #2
Assigned: May-19-2004 Due Date: May-26-2004
General Note:
Homework is due at class time on the Due Date; no late homework will be accepted. Make a COVER PAGE for your homework, including your name and GT numb
ECE 4270 - Summer 2004 Homework Assignment #3
Assigned: May-26-2004 Due Date: June-2-2004
General Note:
Homework is due at class time on the "Due Date"; no late homework will be accepted. Make a COVER PAGE for your homework, including your name and GT nu
Overview of Lecture 3
Review of LTI discrete-time systems
ECE4270
Fundamentals of DSP
Lecture 3
Examples of useful LTI systems
Difference equations
Difference Equations
&
Frequency Response of LTI Systems
Initial rest conditions and LTI
IIR systems
F
Time-Dependent Fourier Transform
Definition:
ECE 4270
Fundamentals of Digital Signal Processing
X [ n, ) =
x[n + m]w[m]e
j m
< n <
m=
w[n]
Lecture 24:
Time Dependent Spectrum Analysis
using Short-Time Fourier Transform
= DTFT of cfw_ x[n + m]w[m]
n
x[
Computational Load for
Difference Equations
ECE 4270
Fundamentals of Digital Signal Processing
Lecture 4:
The Discrete-Time Fourier Transform,
Random Signals
School of Electrical and Computer Engineering
Georgia Institute of Technology
Summer Term, 2002
S
ECE 4270
Fundamentals of Digital Signal Processing
Lecture 3:
Difference Equations,
Frequency Response
School of Electrical and Computer Engineering
Georgia Institute of Technology
Summer Term, 2002
Summer 2003
ECE 4270 M. A. Richards
Copyright 2003
Lectu
ECE 4270
Fundamentals of Digital Signal Processing
Lecture 5:
Random Signals in LSI Systems,
z Transforms
ECE 4270 M. A. Richards
Copyright 2003
Lecture #5, Slide #1
School of Electrical and Computer Engineering
Georgia Institute of Technology
Summer Term
A Fourier Transform Pair
x[n] = e j0 n , 0 n N 1
Lecture 10:
Review of Sampling,
Resolution & Observation Time, &
Digital Processing of C-T Signals
ECE 4270 B. H. Juang
Copyright 2004
sin( 0 ) N / 2) j ( 0 )( N 1) / 2
e
sin( 0 ) / 2)
Analog signal durati
Computation of the DFT
ECE 4270 Fundamentals of Digital Signal Processing
Lecture 22: The Fast Fourier Transform
In order for the DFT to be useful for linear filtering, nonlinear filtering, spectrum analysis, etc., we need efficient computation algorithm
Discrete Signals
ECE 4270 Fundamentals of Digital Signal Processing
6
sample
y
4
2
Sampled Sinusoid 5sin(2nT)
quantize
0
Lecture 2: Discrete-time Signals & Systems, & Properties of LTI Systems
School of Electrical and Computer Engineering Georgia Institut
Discrete Signals
ECE 4270 Fundamentals of Digital Signal Processing
Lecture 8: Sampling
Discrete in time Needs sampling Issue: Under what condition, the original continuous-time signal can be identically recovered or reproduced? Discrete in value Needs q
ECE 4270 Final Exam
Summer 2004 - Prof. B.H. Juang
July 28, 2004
Student Name:_
Test Duration: 2 hrs 50 mins
Problem 1
Consider a stable linear time-invariant system with impulse response h1[n] . The input x[n] and output y[n] satisfy the difference
17
eq