Structure and Interpretation of Systems and Signals
EE 20N

Spring 2012
Problem Set 2 EECS 20N: Structure and Interpretation of Signals and Systems Issued: 11 February 2012 Department of EECS OPTIONAL University of California Berkeley
Circumstances Favorable and Unfavorable to Original Ideas It will be fairly clear to the rea
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Discussion 05: February 27
5.1
CT Integrator
We talked about the continuous time integrator in lecture :
y(t) =
1
T
t
x(s)ds
tT
In lecture we gave you the expression for H(). Lets de
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2012
EECS 20N: Structure and Interpretation of Signals and Systems Problem Set 1 Department of EECS Issued: 26 January 2012 U NIVERSITY OF C ALIFORNIA B ERKELEY Due: 1 February 2012, 5pm
I believe that excessive admiration for the work of great minds is one of
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2012
Problem Set 3 EECS 20N: Structure and Interpretation of Signals and Systems Issued: 2 March 2012 Department of EECS Due: 9 March 2012, 6pm University of California Berkeley
Some people claim a lack of ability for science to justify failure and discouragem
Lab 7: Build your own Shazam
1
Introduction
This lab is about using the DFT to do real audio signal processing. In particular, you will
build a music recognition tool (like Shazam) in MATLAB. You will start out by experimenting
with spectrograms and their
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2012
EECS 20N: Structure and Interpretation of Signals and Systems
Problem Set 4
Department of EECS
Issued: 09 April 2012
U NIVERSITY OF C ALIFORNIA B ERKELEY
Due: 18 April 2012, 6pm
A Hard Days Night
(from www.npr.org)
The jangly opening chord of The Beatles
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
Discussion 03
February 6, 2013
1
1. (a) Express the vector x = 2 as a linear combination of
3
2
1
2
v1 = 1 2 v2 = 1 2 v3 = 1 1 .
3
3
3
1
2
2
1 3 3
(b) Find the inverse of the matrix 1 4 3 .
1 3 4
2. Googles stock prices measured at ve dates are listed b
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 22: April 18
Lecturer: David Tse
22.1
Scribe: S. Zayd Enam
Introduction
This lecture covers:
1. Antialiasing Filter
2. Reconstruction
Were going to elaborate on antialiasing
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 21: April 16
Lecturer: David Tse
21.1
Scribe: Eun Ji An
Agenda
Introduction to Sampling
Down Sampling
Aliasing
Were on to the last part of the course. We only have 3 weeks i
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 20: April 11
Lecturer: Kannan Ramchandran
20.1
Scribe: Steven Chiu
Perception and Representation of Color
Human eyes have receptors to detect three basic colors, so colors are
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 18: April 2
Lecturer: David Tse
18.1
Scribe: KK Lam
Announcement
Midterm on Thursday (4 April)
Topic for today: CTFT
18.2
CTFT
18.2.1
Denition
Let x(t) be aperiodic continuou
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 17: March 21
Lecturer: David Tse
Scribe: Anne Huang
17.1
OFDM
17.1.1
The OFDM Algorithm
Heres the algorithm for OFDM, once again:
1. Take a block of p bits: b(0), b(1), . . . ,
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 15: March 14
Lecturer: David Tse
15.1
Scribe: Hurshal Patel
Agenda
DTFT & DFT review
OFDM
15.2
DFT
Recap from last lecture:
DFT (Davids Fourier Transform): Let 0 =
x(n) =
1
p
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 14: March 12
Lecturer: David Tse
14.1
Scribe: Eun Ji An
Agenda
DTFT
DFT
OFDM  moved to next lecture
Well be talking about the Fourier Transform, specically DTFT (Discrete T
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 13: March 7
Lecturer: David Tse
Scribe: Anne Huang
13.1
Fourier Transform
13.1.1
Warmup: Fourier series is not enough!
Question: compute the Fourier Series of the impulse func
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 12: March 5
Lecturer: David Tse
12.1
Scribe: S. Zayd Enam
Introduction
This lecture covers:
1. FIR and IIR Filters
2. Feedback
3. Magnitude and Phase Response
Thanks for the mi
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 11: February 28
Lecturer: David Tse
11.1
Scribe: Steven Chiu
Composition (Recap.)
Recall the system composed of LTIA and LTIB in cascade. 11.1.
Figure 11.1: Cascade of LTI syst
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 10: February 27
Lecturer: David Tse
10.1
Scribe: KK Lam
Announcement
Topics for today:
Impulse response and convolution
Composition of systems
10.2
Discrete Time Impulse Resp
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 09: February 21
Lecturer: David Tse
9.1
Scribe: Lisa Yan
Announcements
Homework
Homework 04: Posted Friday 2/22, due next Friday 3/1.
Reading: Lee and Varaiya, Chapter 9.
Mid
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 08: February 14th
Lecturer: David Tse
8.1
Scribe: Hurshal Patel
More Examples of Frequency Response
Example 8.1. Foucault Pendulum (cont.)
y(t)
r
x(t)
mg
Figure 8.1: Focault pe
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 07: February 12
Lecturer: David Tse
7.1
Scribe: Eun Ji An
Announcements
Homework
Homework 3 due on Friday, February 15th
There will be no new homework assigned on Friday, Feb
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 23: April 23
Lecturer: David Tse
23.1
Scribe: Lisa Yan
Agenda
Questions on sampling
Interpolation strategies: timedomain view
Eects of sampling in the frequency domain
An
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 24: April 25
Lecturer: David Tse
24.1
Scribe: Hurshal Patel
Agenda
Recap of sampling
Application: Downsampling
24.2
Recap of sampling
Recall from last lecture the sampling an
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Lecture 25: April 30
Lecturer: David Tse
25.1
Scribe: S. Zayd Enam
Introduction
This lecture will review and cover more topics on sampling. It seems that students are having the
most d
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Discussion 7: March 13
7.1
Feedback System
Given a causal feedback LTI system as shown in Fig 7.1 with F (w) = 1 ei2w .
4
Figure 7.1: Feedback system
a) Find the frequency response of
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Discussion 13: May 1
13.1
Multirate Sampling
1. xu (n) has a sampling rate of fs L.
xd (n) has a sampling rate of fs /M .
2. L and M must be integer valued by denition. If M Z, then nM
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Discussion 13: May 1
13.1
Multirate Sampling
Suppose you were recording a song in your music studio with high end audio equipment that records
at a sampling rate of 48 kHz. You want to
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
Discussion
April 17, 2013
Outline
2D Fourier Transform
Digital Camera
2D Filtering and downsampling
2D Fourier Transform
Question:
Matching
Black means small magnitude
White means high magnitude
2D Fourier Transform
Answer:
Matching
Black means smal
Structure and Interpretation of Systems and Signals
EE 20N

Spring 2013
EE20N: Structure and Interpretation of Systems and Signals
Spring 2013
Discussion 04: February 13
4.1
Introduction
1. TimeInvariance
2. LTI Systems
4.2
TimeInvariance
Determine whether the following systems are timeinvariant:
a) y(t) = x(t)
1
b) y(n) =