Equalization
Prof. David Johns
University of Toronto
(johns@eecg.toronto.edu)
(www.eecg.toronto.edu/~johns)
University of Toronto
slide 1 of 70
D.A. Johns, 1997
Adaptive Filter Introduction
Adaptive filters are used in:
Noise cancellation
Echo cancellat

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout x
Homework 2
EE 327 Signal Processing
Aug 13, 2010
Question 1) Let us try to understand superposition and homogeneity in the denition of
LTI systems.
a) First show that superposi

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout x
Lecture Notes 2
EE 327 Signal Processing
Aug 24, 2010
Fourier Series
We have come across the term Fourier Series in the last chapter. This is a term so dear
to Signal Processin

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout 3
Lecture Notes 1
EE 327 Signal Processing
July 24, 2009
Introduction
1
Signals
A collection of sensible objects
Merriam Webster (http:/m-w.com) has the following info.
Main En

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout x
Homework 3
EE 327 Signal Processing
Aug 20, 2010
Question 1) Consider a periodic signal f (t). The Fourier Series expansion coecients are
obtained by
1
fm =
T
+T
2
2
f (t)ej T

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout x
Home work 6
EE 327 Signal Processing
Oct 3, 2010
Question 1) Parsevals Theorem for the DFT: Show that
N 1
N 1
2
|x[n]|2
|X[k]| = N
(1)
n=0
k=0
where X[k] is the N point DFT giv

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout x
Homework 4
EE 327 Signal Processing
Aug 27, 2010
Question 1) Consider a T -periodic signal x(t) shown in gure. This is known as the
rectangular train, where the non-zero amplit

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout x
Homework 5
EE 327 Signal Processing
Sep 3, 2010
Question 1) Consider a complex signal x(t), which happens to be symmetric, i.e.
x(t) = x (t)
Show that its Fourier Transform X(f

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout 8
Lecture Notes 3 (updated)
1
EE 327 Signal Processing
Aug 5, 2009
Transform or Series
We have made some progress in advancing the two concepts of Fourier Series and Fourier
Tran

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout
Homework 7
EE 327 Signal Processing
Oct 19, 2010
Question 1) The Discrete Fourier Transform or DFT is dened as
N 1
X[k] =
x[n] exp(j
n=0
2
nk).
N
(1)
a) What is the DFT of the se

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout x
Lecture Notes 4
1
EE 327 Signal Processing
Nov 6 , 2010
Discrete-Time Fourier Transform (DTFT)
We have seen some advantages of sampling in the last section. We showed that by c

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Handout x
Lecture Notes 5
1
EE 327 Signal Processing
Nov 13 , 2010
Practical Filter Design
We will now apply the Fourier representations that we learned to design lters. Designing
lters

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Mid Sem
|20| + |10| + |45| = 75marks
EE 327 Signal Processing
September 15, 2010
Instructions
1. Spend time in understanding the questions.
2. Crisp answers are preferred ( 3 lines for a