Solution Manual for Adaptive Filter Theory, 5th Edition

Name: Solution Manual for Adaptive Filter Theory, 5th Edition
Brand: Academic Documents Platform
Price: 15 USD
Availability: InStock
Author: Seller Steve

Solution Manual for Adaptive Filter Theory, 5th Edition provides you with expert textbook solutions that ensure you understand every concept thoroughly.

Seller Steve

Contributor

4.6

2 days ago

Preview (16 of 423)

Solution Manual
for
Adaptive Filter Theory 5e
Created by
Simon Haykin
and
Kelvin Hall
McMaster University
HAMILTON, ONTARIO
CANADA

Table of Contents
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P ii
Corrections for Question-Descriptions in the Textbook . . . . . . . . . . . . . . P iv
Notes on Computer Simulations and Provided Programs . . . . . . . . . . . . P vi
Chapter 1: Stochastic Processes and Models . . . . . . . . . . . . . . . . . . . . . . . . P 1
Chapter 2: Wiener Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 21
Chapter 3: Linear Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 48
Chapter 4: Method of Steepest Descent . . . . . . . . . . . . . . . . . . . . . . . . . . P 102
Chapter 5: Method of Stochastic Gradient Descent . . . . . . . . . . . . . . . . P 120
Chapter 6: The Least-Mean-Square(LMS) Algorithm . . . . . . . . . . . . . . P 128
Chapter 7: Normalized Least-Mean-Square(LMS) Algorithm
and Its Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 167
Chapter 8: Block-Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 178
Chapter 9: Method of Least-Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 190
Chapter 10: The Recursive Least-Squares (RLS) Algorithm . . . . . . . . P 214
Chapter 11: Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 229
Chapter 12: Finite-Precision Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 243
Chapter 13: Adaptation in Nonstationary Environments . . . . . . . . . . . . P 251
Chapter 14: Kalman Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 304
Chapter 15: Square-Root Adaptive Filtering Algorithms . . . . . . . . . . . P 324
Chapter 16: Order-Recursive Adaptive Filtering Algorithm . . . . . . . . P 341
Chapter 17: Blind Deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 380
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P 394
iii

Notes on the Computer Simulations and Provided Programs
The computer experiments completed for this solutions manual were completed al-
most exclusively using Matlab®, for ease of readability. To improve the accessibility of
the solutions, to the users of this manual, specialized signal processing toolkits were not
used in programs included. Graphical solutions are provided along with the .m files in
case the user of the textbook is interested in completing the exercises in a different pro-
gramming language, in which case a graphical solution is available for comparison.
The solutions of the computer problems in Chapter 13 were completed by Ashique
Rupam Mahmood, Computer Science, University of Alberta, the creator of the Autostep
algorithm. The solutions being completed prior to the rest of the manual are only avail-
able in the programming language python, which is similar to Matlab® and therefore quite
readable.
vi

Chapter 1
Problem 1.1
Let
ru(k) = E[u(n)u∗(n − k)] (1)
ry(k) = E[y(n)y∗(n − k)] (2)
we are given that
y(n) = u(n + a) − u(n − a) (3)
Hence, substituting Equation (3) into Equation (2), and then using Equation (1), we get
ry(k) =E[(u(n + a) − u(n − a))(u∗(n + a − k) − u∗(n − a − k))]
=2ru(k) − ru(2a + k) − ru(−2a + k)
Problem 1.2
We know that the correlation matrix R is Hermitian; that is to say that
RH = R
Given that the inverse matrix R−1 exists, we may write
R−1RH = I
where I is the identity matrix. Taking the Hermitian transpose of both sides:
RR−H = I
1

PROBLEM 1.3. CHAPTER 1.
Hence,
R−H = R−1
That is, the inverse matrix R−1 is Hermitian.
Problem 1.3
For the case of a two-by-two matrix, it may be stated as
Ru = Rs + Rν
=
[r11 r12
r21 r22
]
+
[σ2 0
0 σ2
]
=
[r11 + σ2 r12
r21 r22 + σ2
]
For Ru to be nonsingular, we require
det(Ru) 6 = 0
(r11 + σ2)(r22 + σ2) − r12r22 6 = 0
With r12 = r21 for real data, this condition reduces to
(r11 + σ2)(r22 + σ2) − r2
12 6 = 0
Since this is a quadratic in σ2, we may impose the following conditions on σ2 for nonsin-
gularity of Ru:
σ2 6

Loading page 6...

PROBLEM 1.5. CHAPTER 1.
This matrix is positive definite because it satisfies the condition:
aT R a = [a1 a2
] [1 1
1 1
] [a1
a2
]
=a2
1 + 2a1a2 + a2
2
=(a1 + a2)2 > 0 for all nonzero values of a1 and a2
But the matrix R is singular because:
det(R) = (1)2 − (1)2 = 0
Hence, it is possible for a matrix to be both positive definite and singular at the same time.
Problem 1.5
a)
RM +1 =
[r(0) rH
r RM
]
(1)
Let
R−1
M +1 =
[a bH
b CM
]
(2)
wherea, b and C are to be determined. Multiply Equation (1) by Equation (2):
IM +1 =
[r(0) rH
r RM
] [a bH
b C
]
Where IM +1 is the identity matrix. Therefore,
r(0)a

Loading page 7...

Loading page 8...

Loading page 9...

Loading page 10...

Loading page 11...

Loading page 12...

Loading page 13...

Loading page 14...

Loading page 15...

Loading page 16...

15 more pages available. Scroll down to load them.

Preview Mode

100%

Study Now!

XY-Copilot AI

Unlimited Access

Secure Payment

Instant Access

24/7 Support

Document Chat

Document Details

Subject

Electrical Engineering & Electronics

Solution Manual for Adaptive Filter Theory, 5th Edition

Study Now!

Document Details

Related Documents

Flip-Flop Timing Parameters and Circuit Behavior Analysis

Bridge Rectifier and its Analysis: A Study of Output Voltage and Ripple Effects

FM Receiver Design and Functionality: Analysis of Key Stages and Components Week 6 Assignment

Test Bank for Elemental Geosystems, 9th Edition

Solution Manual for Electrical Engineering: Principles and Applications, 7th Edition

Solution Manual for Analog Integrated Circuit Design, 2nd Edition

Solution Manual for Advanced Semiconductor Fundamentals, 2nd Edition

Solution Manual For Introductory Circuit Analysis, 12th Edition

Solution Manual For Electronics, 2nd Edition

Engineering Electromagnetics, 8th Edition Solution Manual

Company

Explore

Study Tools