University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 2
FALL 2012
Issued: Thursday, 13 September 2012
Due: Thursday, 20 September 2012
Problem 1.1 (Periodic Signals)
Determine whether the fo
ECE 330: Signals and Systems
Fall 2012
Lecture 6 September 20
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Introduction to systems
System properties
Memoryless: A system is memoryless if the output value at any time does not
depend on in
ECE 330: Signals and Systems
Fall 2012
Lecture 7 September 25
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Time-invariance
Examples of system properties
Lecture Outline:
Putting linearity and time-invariance together.
7.1
Linear Time-Inv
ECE 330: Signals and Systems
Fall 2012
Lecture 8 September 27
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Putting linearity and time-invariance together.
Lecture Outline:
Convolution sum and convolution integral (DT and CT, respectively)
ECE 330: Signals and Systems
Fall 2012
Lecture 9 October 2
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Convolution sum and convolution integral (DT and CT, respectively)
Lecture Outline:
Impulse response of an RC circuit and example
CT
ECE 330: Signals and Systems
Fall 2012
Lecture 10 October 4
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
CT convolution
Impulse response of an RC circuit and example
Properties of LTI systems: commutativity / associativity/ distributivit
ECE 330: Signals and Systems
Fall 2012
Lecture 11 October 9
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
System properties of LTI systems.
Step response.
Lecture Outline:
Putting complex exponentials through linear time-invariant systems
ECE 330: Signals and Systems
Fall 2012
Lecture 12 October 11
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Complex exponentials are eigenfunctions of LTI systems.
Continuous time Fourier series (CTFS).
Lecture Outline:
CTFS example: the s
ECE 330: Signals and Systems
Fall 2012
Lecture 14 October 23
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
CTFS example: the square wave.
Convergence of CTFS.
Discrete time Fourier series (DTFS).
Today:
Recap of DTFS synthesis equation.
ECE 330: Signals and Systems
Fall 2012
Lecture 15 October 25
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Recap of DTFS synthesis equation.
Derivation of DTFS analysis equation.
Examples.
Today:
Fourier analysis of aperiodic signals.
I
ECE 330: Signals and Systems
Fall 2012
Lecture 16 October 30
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Fourier analysis of aperiodic signals. (An aperiodic signal is a periodic signal with
T .)
Square wave example.
Fourier transform a
ECE 330: Signals and Systems
Fall 2012
Lecture 17 November 1
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Finish examples.
Convergence of Fourier transform.
Fourier transform of periodic signals.
Today
Fourier transform properties:
Lin
ECE 330: Signals and Systems
Fall 2012
Lecture 5 September 18
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Riemann approximation, unit pulse and impulse, unit step
Sinusoids and complex exponentials
Unit impulse and complex exponentials
ECE 330: Signals and Systems
Fall 2012
Lecture 4 September 13
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Lecture Outline:
Riemann approximation to CT signals
Sinusoids and complex exponentials
Introduction to systems
System properties
4.1
Rieman
ECE 330: Signals and Systems
Fall 2012
Lecture 3 September 11
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Lecture Outline:
CT signals
DT signals
Basic signal characteristics/ manipulations
Unit impulse and Riemann sums
In this lecture we will lea
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 3
FALL 2012
Issued: Thursday, 20 September 2012
Due: Thursday, 27 September 2012
Note: the fun part of this problem set is Problem 1.7
P
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 4
FALL 2012
Issued: Thursday, 27 September 2012
Due: Thursday, 04 October 2012
Problem 1 (System Properties I)
Are the following systems
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 5
FALL 2012
Issued: Thursday, 04 October 2012
Due: Thursday, 11 October 2012
Problem 1 (Discrete Time Convolution)
Evaluate the followin
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 6
FALL 2012
Issued: Thursday, 18 October 2012
Problem 1 (Fourier Series Warm-up)
Given a signal x(t) = 0.5 + 0.2 cos t + sin
2
Due: Thur
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 7
FALL 2012
Issued: Thursday, 25 October 2012
Due: Thursday, 01 November 2012
Problem 1 (DTFS Analysis)
Use the denition equation for th
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 8
FALL 2012
Issued: Thursday, 01 November 2012
Due: Thursday, 09 November 2012
Problem 1 (CTFT Properties)
Find the Fourier transform of
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 9
FALL 2012
Issued: Thursday, 22 November 2012
Problem 1 (RC Circuit)
Suppose signal Vr (t) = sin 200t +
shown in Figure 1.
4
Due: Thurs
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 10
FALL 2012
Issued: Thursday, 29 November 2012
Due: Thursday, 06 December 2012
Problem 1 (Image Processing using MATLAB)
(This MATLAB p
University of Wisconsin, Madison
Department of Electrical and Computer Engineering
330 SIGNALS AND SYSTEMS
Problem Set 11
FALL 2012
Issued: Thursday, 06 December 2012
Due: Thursday, 13 December 2012
Last homework set this semester. Hooray!
Problem 1 (Samp
INTRODUCTION TO MATLAB
ECE 330: Signal and Systems, 2012 Fall
Yanpei (Nick) Liu
https:/sites.google.com/site/yanpeiliu/
Electrical and Computer Engineering
University of Wisconsin, Madison
(2012 Fall)
Yanpei (Nick) Liu (UW-Madison)
Intro to MATLAB
2012 Fa
ECE 330: Signals and Systems
Fall 2012
Lecture 1 September 4
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Lecture Outline:
Administrative details
What are signals and systems?
Motivating examples
Course themes
In this course well learn about a pow
ECE 330: Signals and Systems
Fall 2012
Lecture 18 November 6
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Fourier transform properties.
Today
Parsevals relation.
Convolution property.
Filtering and examples.
Partial fraction expansion.
ECE 330: Signals and Systems
Fall 2012
Lecture 19 November 8
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Parsevals relation.
Convolution property.
Filtering and examples.
Partial fraction expansion.
Today
RC-circuits as lters.
Using
Signals: The Basics
Key Concepts
1) Signals are represented as functions of one or more independent
variables.
a) In continuous-time signals the independent variable can
take on any possible value.
b) In discrete-time signals the independent variable can
Frequency-Domain Descriptions for
Continuous-Time Linear Time-Invariant Systems
Copyright c Barry Van Veen 2015
Key Concepts
1) Frequency response H() is the Fourier transform of the impulse
response.
a) The magnitude response is |H()|.
b) The phase respo