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Adaptive Filter Design PDF

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Added on  2021-12-13

Adaptive Filter Design PDF

   Added on 2021-12-13

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Solution 1
a)
As per the theory the filtering will be ok here as we can easily remove overlapping noise through
filter processing. In case if we apply filtering then two popular filtering method of adaptive
nature, namely noise cancellation in adaptive manner and signal enhancement in adaptive
manner, are perfect techniques for processing this.
b) Now we can have
Design:
Transfer function of filter is:
H ( z )= Y ( z )
X ( z ) =

k=0
M
bk zk
1+
k=0
N
ak z k
So here M is the fir filter length. Order of filter is given by N=M-1.
Response of filter is
y ( n )=
k=0
M 1
bk x (nk )
y ( n )=
k=0
M 1
h( k) x (nk )
Coefficients:
Without Window
b = 0.0169 0.2528 0.5667 0.2528 0.0169
Adaptive Filter Design  PDF_1
Rectangular Window
b = 0.0169 0.2528 0.5667 0.2528 0.0169
At 95% unity**, the poles are:
p1, 2=. 95[. 5878± j .8090
p1, 2=.5584± j . 7686
H ( z )= ( z.5878+ j. 8090 )( z.5878 j . 8090)
( z. 5584+ j. 7686 )( z.5584 j. 7686 )
With the reduced canonical form:
H ( z )= 11. 175 z1+ z2
11 .117 z1+. 903 z2
The recursive algorithm becomes:
yn=xn1. 175 xn1+ xn2+ 1. 117 yn1. 903 yn2
Output:
Without Window
Adaptive Filter Design  PDF_2
Rectangular Window
Adaptive Filter Design  PDF_3
c)
Zeroes of the functions are:
z1, 2=cos( 54 ° )± jsin( 54 ° )
z1, 2=.5878± j . 8090
Adaptive Filter Design  PDF_4

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