adaptive predictor computer experiments
DESCRIPTION
Matlab program for adaptive equalizerTRANSCRIPT
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Z-
1
Σ
u(n) u(n-1)
)1()(ˆ −nunw
)(ˆ nw
f(n)-
+
LMS Algorithm - ComputerExperiments
Experiment 1: Adaptive Predictor
AR(1) Process
Autoregressive process of order 1 is dened as
u (n )=−au (n−1 )+v (n)
!here"
'a' is the parameter of A#$1% process
'v(n)' is &'( !ith variance σ v2
Adaptive First order Predictor
Fig 1: Adaptive First order Predictor
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LMS !eight update e)uation is
w (n+1 )=w (n )+ μu (n−1 ) f (n)
f (n )=u (n )−w (n ) u(n−1)
Experiment Results
Experiment is carried out !ith the follo!ing cases
Case1:
a* -,
.ariance of u$n%* ,/02
Case2:
a* +,
.ariance of u$n%* ,3
4he Step si5e parameter is ta6en as µ*,3 and initial condition w (0 )=0
Steps:
1, 'enerate A# process
u (n )=−au (n−1 )+v (n)
, 7nitiali5e w (0 )=0
/, 8pdate w (n )
w (n+1 )=w (n )+ μu (n−1 ) f (n)
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f (n )=u (n )−w (n)u(n−1)
9, #epeat step / for 3 iterations,
3, #epeat steps 1 to 9 for 1 times and compute ensem:le average of
w (n )
;igure sho!s the transient :ehavior of w (n ) , 7t also sho!s the
E (w (n ) ) o:tained :< the ensem:le averaging of 1 independent trials,
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4he experimental learning curves of adaptive rst order prediction for
var<ing step si5e parameter is sho!n in ;ig,
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Problem 5.21
AR(2) Process
Autoregressive process of order is dened as
u (n )=−a1u (n−1 )±a
2u (n−1 )+v (n)
a1=0.1
a2=−0.8
a) Noise variance σ v2
such that σ u2
=1
σ v2=
(1−a2) ((1+a2 )2−a
1
2)(1+a2 )
σ u2
σ v2=0.27
Matlab Code for different realization of u(n)
var_v=(1-a2)*((1+a2)^2-a1^2)/(1+a2);
% initial values of u(n)u(1)=var_v*randn(1,1); %u(2)=-a1*u(1)+var_v*randn(1,1);
for n=3:N
u(n)=-a1*u(n-1)-a2*u(n-2)+var_v*randn(1,1);end
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