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Instructor’s Guide to Accompany Digital Signal Processing: Fundamentals and Applications Part 2: Chapter 9 – Chapter 14 Lizhe Tan Jean Jiang

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Digital Signal Processing

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Digital Signal Processing

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Digital Signal Processing

Instructor’s Guide to Accompany Digital Signal Processing: Fundamentals and ApplicationsnPart 2: Chapter 9 – Chapter 14 Lizhe Tan Jean Jiang

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digital signal processing
digital signal processing fundamentals and applic
fundamentals and applications third edition

Institution Digital Signal Processing
Course Digital Signal Processing

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Instructor’s
Tan andGuide to Accompany
Jiang’s Instructor’s Guide to Accompany to Digital Signal Processing 1
Digital Signal Processing: Fundamentals and Applications
Part 2: Chapter 9 – Chapter 14

Instructor’s Guide to Accompany

Digital Signal Processing: Fundamentals and Applications
Part 2: Chapter 9 – Chapter 14

Lizhe Tan
Jean Jiang

,Tan and Jiang’s Instructor’s Guide to Accompany to Digital Signal Processing 2

Chapter 9

9.1
dJ
 40  10  2 w  0 , w*  2
dw
J min  J |ww*  50  40w  10w2 |w1  50  40  2  10  22  10
9.2
dJ
 20  10  2w  0 , w*  1
dw
J min  J |ww*  15  20w  10w2 |w1  15  20  (1)  10  (1)2  5

9.3
dJ
 20  2  2 w  0 , w*  5
dw
J min  J |ww*  100  20w  2w2 |w1  100  20  (5)  2  (5) 2  50

9.4
dJ
 30  2  15w  0 , w*  1
dw
J min  J |ww*  10  30w  15w2 |w1  10  30 1  15 12  5

9.5
dJ
 40  20w
dw
dJ dJ
  0.04   40  20w0  |w0 0  1.6 , w1  w0    0   1.6   1.6
dw dw
dJ dJ
  0.04   40  20w1  |w1 1.6  0.32 w2  w1    1.6   0.32   1.92
dw dw
dJ dJ
  0.04   40  20w2  |w2 1.92  0.064 w3  w2    1.92   0.064   1.984
dw dw
J min  40  20w  10w2 |w0.992  50  40 1.984  10 1.9842  10.0026
w*  w2  1.984 , and J min  10.0026

9.6
dJ
 20  20w
dw
dJ dJ
  0.04   20  20 w0  |w0 0  0.8 , w1  w0    0   0.8   0.8
dw dw
dJ dJ
  0.04   20  20w1  |w1 0.8  0.16 w2  w1    0.8   0.16   0.96
dw dw

,Tan and Jiang’s Instructor’s Guide to Accompany to Digital Signal Processing 3

dJ dJ
  0.04   20  20w2  |w2 0.96  0.032 w3  w2    0.96   0.032   0.992
dw dw
J min  40  20w  10w2 |w0.992  15  20  (0.992)  10  (0.992)2  5.00064
w*  w3  0.992 , and J min  5.00064

9.7
dJ
 20  4 w
dw
dJ dJ
  0.2   20  4 w0  |w0 4  0.8 , w1  w0    4   0.08   4.8
dw dw
dJ dJ
  0.2   20  4 w1  |w1 4.8  0.16 w2  w1    4.8   0.16   4.96
dw dw
dJ dJ
  0.2   20  4 w2  |w2 4.96  0.032 w3  w2    4.96   0.032   4.992
dw dw
J min  100  20w  2w2 |w4.992  100  20  (4.992)  2  (4.992)2  5.0001
w*  w3  4.992 , and J min  5.0001

9.8
dJ
 30  30w
dw
dJ dJ
  0.02   30  30 w0  |w0  2  0.6 , w1  w0    2   0.6   1.4
dw dw
dJ dJ
  0.02   30  30 w1  |w1 1.4  0.24 w2  w1    1.4   0.24   1.16
dw dw
dJ dJ
  0.02   30  30w2  |w2 1.16  0.096 w3  w2    1.16   0.096   1.064
dw dw
J min  10  30w  15w2 |w1.064  10  30  (1.064)  15  (1.064) 2  4.93856
w*  w3  1.064 , and J min  4.93856

9.9
a.
y(n)  w0 x(n)  w1 x(n  1)
e(n)  d (n)  y (n)
w0  w0  0.2  e(n) x(n)
w1  w1  0.2  e(n) x(n  1)
b.
for n  0 : y (0)  0 , e(0)  3 , w0  1.8 , w1  1
for n  1 : y (1)  1.2 , e(1)  3.2 , w0  2.44 , w1  0.92
for n  2 : y (2)  5.8 , e(2)  4.8 , w0  0.52 , w1  0.04

, Tan and Jiang’s Instructor’s Guide to Accompany to Digital Signal Processing 4

c.
W  [0 0]T , X (n)  [ x(n) x(n  1)]T
1 0 
Q   
0 1 
  d (n)  X T (n)W
QX (n)
k
  X T (n)QX (n)
W  W  k
Q  [Q  kX T (n)Q]/ 
y ( n)  W T X ( n )
e(n)  d (n)  y (n)
d.

close all; clear all; clc
W=[0 0]'; X=[0 0]';
x=[3 -1 2]; d=[3 -2 1]; y=[];
lamda=0.96; delta=0.5;Q=eye(2)*delta;
for n=1:3
X=[x(n); X(1:1)];
alpha=d(n)-X'*W
k=Q*X/(lamda+X'*Q*X)
W=W+k*alpha
Q=(Q-k*X'*Q)/lamda
y(n)=W'*X
e(n)=d(n)-y(n)
end

n=0:
alpha = 3
k = 0.2747
0
W = 0.8242
0
Q = 0.0916 0
0 0.5208
y = 2.4725
e = 0.5275
n=1:
alpha = -1.1758
k = -0.0160
0.2723
W = 0.8429
-0.3201
Q = 0.0939 0.0260
0.0260 0.0994

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