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
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 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 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 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
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 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
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
ECE 330: Signals and Systems
Fall 2012
Lecture 21 November 20
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
RC-circuits as lters.
Using the convolution property to calculate the output of an LTI lter.
Partial fraction expansions.
The mul
ECE 330: Signals and Systems
Fall 2012
Lecture 22 November 27
Lecturer: Stark Draper
Scribe: Shirzad Malekpour
Last Time:
Discrete-time Fourier transform (DTFT) and examples.
DTFTs of periodic signals.
Today
Examples of the DTFT of DT periodic signals.
Introduction to Sampling and Reconstruction
Key Concepts
1) Sampling is used to convert signals in the physical world with continuous independent variables (e.g., time) to a sequence of numbers
that can be processed by a computer.
2) Reconstruction is use