Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
The Laplace Transform
Motivation
Frequency-domain analysis is based on representing signals as linear combinations of eigenfunctions
of linear ti
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Homework 3, due Friday, April 25
There are six problems. Problems 3, 4 and 5 involve MATLAB.
1.
Sampling and signal energy.
A continuous-time sig
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Homework 6, due Friday, May 16
Laplace Transform Problems
1.
2.
Determine the signal x t for each of the following Laplace transforms and associa
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Homework 4, due Friday, May 2
1. DFTs of simple sequences.
Given these 8-point signals xn , n 0, , 7 , compute the 8-point DFTs X k , k 0, , 7 .
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Homework 9
Not to be turned in for a grade. Solutions will be made available by Friday, June 6.
Laplace Transform and Feedback Control Problem
1.
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Homework 5
Not to be turned in for a grade. Solutions will be made available on Wednesday, May 7.
Laplace Transform Problems
Match each Laplace t
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #09
Assigned: May 29, 2013
Due Date: June 5, 2013
Reading: Chapters 7 and 8 of SP-First and Chapter 10 of S&S.
= Please check the Class2Go Forum often. All ocial cour
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #08
Assigned: May 22, 2013
Due Date: May 29, 2013
Reading: Chapters 7 and 8 of SP-First and Chapter 10 of S&S.
= Please check the Class2Go Forum often. All ocial cour
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #7
Assigned: May 15, 2013
Due Date: May 22, 2013
Reading: Notes posted on the website as Chapter 66 and Chapter 13 of SP-First.
= Please check the Class2Go Forum ofte
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #6
Assigned: May 10, 2013
Due Date: May 15, 2013
Reading: Notes posted on the website as Chapter 66 and lecture slides on decimation and interpolation and the DFT.
=
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #5
Assigned: May 1, 2013
Due Date: May 8, 2013
Reading: In SP-First, Chapter 6 on the frequency response and notes posted on the website as
Chapter 66. Also, the Warm
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #4
Assigned: April 24, 2013
Due Date: May 1, 2013
Reading: In DSP First, Chapter 6 on the frequency response and notes posted on the website as
Chapter 66.
= Please c
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Homework 8, due Friday, May 30
Problems on Z Transforms and Discrete-Time LTI Systems
1.
The z transform of xn is
X z
1 z 1
.
1 13 z 1
Without c
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Homework 7, due Friday, May 23
Laplace Transform and Feedback Problems
1.
Poles and zeros of a matched filter.
Matched filtering is used in many
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Homework 2, due Friday, April 18
Discrete-Time Signals and Systems
1.
Given a signal
3
xn 2 cos n sin n ,
4
8
sketch the real and imagin
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
The Z Transform
Motivation
In discrete time, as in continuous time, frequency-domain analysis is based on representing signals as
linear combinat
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
The Discrete Fourier Transform
Motivations for the Discrete Fourier Transform
Numerical Fourier analysis requires a Fourier representation that i
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Communication Systems
Communication Media
c
2
Approximate Carrier Frequency
Medium
Digital subscriber lines
44000 kHz
Broadcast AM radio
5401610
EE 102B: Signal Processing and Linear Systems II
Professor J. M. Kahn, Stanford University
Chapter 4: Frequency-Domain Representation of Discrete-Time
Signals
Motivation: Complex exponentials are eigenfunctions of linear time-invariant systems. We conside
EE 102B: Signal Processing and Linear Systems II
Professor J. M. Kahn, Stanford University
Chapter 3: Time-Domain Analysis of Discrete-Time Systems
Denition: A discrete-time system H acts on an input x[n] to yield an output y[n]:
Hcfw_x[n] = y[n]
x>n@
y>n
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Sampling and Reconstruction
Terminology Used Here
Sampling is the conversion of a continuous-time signal (which is usually not quantized) to a di
EE 102B: Signal Processing and Linear Systems II
Professor J. M. Kahn, Stanford University
Chapter 2: Time-Domain Representation of Discrete-Time Signals
Discrete-Time Sinusoids
Periodicity
Start with continuous-time sinusoid:
x(t) = A cos(0 t + )
<t<
Co
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Finite Impulse Response Discrete-Time Filters
Subjects We Address Here
Applications of discrete-time signal processing.
Types of discrete-time fi
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Infinite Impulse Response Discrete-Time Filters
Subjects We Address Here
Types of discrete-time filters: FIR and IIR (review).
Design of IIR disc
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Feedback Systems
Based in part on Professor John Paulys notes from EE 102A, Winter 2012-13.
Applications and Consequences of Feedback
Control Sys
Stanford University
EE 102B: Signal Processing and Linear Systems II
Spring 2013-14, Professor Joseph M. Kahn
Notation
Frequence Variable
Case
EE 102B Course
Notes
Oppenheim, Willsky,
Nawab
Oppenheim, Schafer
Continuous time
(rad/s)
(rad/s)
(rad/s)
Dis
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #3
Assigned: April 17, 2013
Due Date: April 24, 2013
Reading: In DSP First, Chapter 6 on the frequency response and notes posted on the website as
Chapter 66.
= Pleas
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #2
Assigned: April 10, 2013
Due Date: April 17, 2013
Reading: In SP First, Chapter 5 on FIR Filters and Chapter 6 on Frequency Response.
= Please check the Bulletin B
STANFORD UNIVERSITY
DEPARTMENT of ELECTRICAL ENGINEERING
EE 102B
Spring 2013
Problem Set #1
Assigned: April 3, 2013
Due Date: April 10, 2013
Reading: In SP First, Review Chapters 9-12 .
= Please check the Class2Go website often. All ocial course announcem
STANFORD UNIVERSITY
EE 102B
Spring-2013
ASSIGNMENTS
! Reading for this Lecture:
! SPF: Sections 66-1, 66-2, 66-3 & 66-4 (notes
posted on Course2Go website)
! Lab 04 Warm-Up section
! S&S: Chapter 5
Lecture 12
FIR Filter Design
April 26, 2013
! HW#04 is du