Homework SourseAdaptive Algorithms i need a matlab code for itSolution1 Pro
Adaptive Algorithms
i need a matlab code for it
Solution
1) %Program to illustrate adaptive filtering using the LMS algorithms:
% X delayed input data vector
% Y measured signal
% W coefficient vector
% E enhanced signal
N=30; % filter length
M=0; % delay
w0=1; % initial value for adaptive filter coefficients
SF=2048; % factor for reducing the data samples - 11 bit ADC assumed
mu=0.04;
X = zeros(N,1);
delay = zeros(1,M+1);
W = w0*ones(N,1);
in = fopen(\'ADF.dat\',\'r\'); %read input data from specified data file
Y = fscanf(in,\'%g\',inf)/SF;
fclose(in);
if w0==0
sf = SF; % scaling factor for display
else
sf = SF/N/w0;
end
for i=1:length(Y)
if M>0
delay(2:M+1) = delay(1:M); % shift data for delay
end
delay(1) = Y(i);
X(2:N) = X(1:N-1); % update buffer
X(1) = delay(M+1);
E(i) = Y(i)-W\'*X; % the enhanced signal
W = W + 2*mu*E(i)*X; % update the weights
end
subplot(2,1,1),plot(1:length(Y),Y*SF); title(\'Input Signal\');
subplot(2,1,2),plot(1:length(E),E*sf); title(\'Enhanced Signal\');
2) % program to illustrate adaptive filtering using the RLS algorithm via the UDU factorization:
% X delayed input data vector
% Y measured signal
% W coefficient vector
% E enhanced signal
clear all;
N = 30; % filter length
M = 1; % delay
npt = N*(N+1)/2;
SF = 2048; % 12-bit ADC scaling
p0 = 0.05;
w0 = 1;
gamma = 0.98;
RemoveMean = 0; % 1 - remove the mean from the data, 0 - otherwise
delay = zeros(1,M);
U=zeros(1,npt);
U(1)=p0;
W = w0*ones(N,1);
X = zeros(N,1);
for i=1:N-1
ik=(i*(i+1)-2)/2+1;
U(ik)=p0;
end
if w0==0
sf = SF; % scaling factor for display
else
sf = SF/N/w0;
end
in = fopen(\'ADF.dat\',\'r\'); %read input data from specified data file
Y = fscanf(in,\'%g\',inf)/SF;
fclose(in);
if RemoveMean % remove the mean from the data if required
Y = Y - sum(Y)/length(Y);
end
for i=1:length(Y)
if M>0
delay(2:M+1) = delay(1:M); % shift input data in delay registers
end
delay(1) = Y(i);
X(2:N) = X(1:N-1); % update buffer
X(1) = delay(M+1);
E(i) = Y(i) - X\'*W; % the enhanced signal
W = uduflt(W,X,U,E(i),gamma ,N);
end
subplot(2,1,1),plot(1:length(Y),Y*SF); title(\'Input Signal\');
subplot(2,1,2),plot(1:length(E),E*sf); title(\'Enhanced Signal\');
3) % program to illustrate adaptive filtering using the square root RLS algorithm:
% X delayed input data vector
% Y measured signal
% W coefficient vector
% E enhanced signal
N = 30; % filter length
M = 1; % delay
npt = N*(N+1)/2;
SF = 2048; % 12-bit ADC scaling
p0 = 0.05;
w0 = 1;
gamma = 0.98;
RemoveMean = 0; % 1 - remove the mean from the data, 0 - otherwise
delay = zeros(1,M);
W = w0*ones(N,1);
X = zeros(N,1);
S = zeros(1,npt);
S(1)=p0;
for i=1:N-1
ik=(i*(i+1)-2)/2+1;
S(ik)=p0;
end
if w0==0
sf = SF; % scaling factor for display
else
sf = SF/N/w0;
end
in = fopen(\'ADF.dat\',\'r\'); %read input data from specified data file
Y = fscanf(in,\'%g\',inf)/SF;
fclose(in);
if RemoveMean % remove the mean from the data if required
Y = Y - sum(Y)/length(Y);
end
for i=1:length(Y)
if M>0
delay(2:M+1) = delay(1:M); % shift input data in delay registers
end
delay(1) = Y(i);
X(2:N) = X(1:N-1); % update buffer
X(1) = delay(M+1);
E(i) = Y(i) - X\'*W; % the enhanced signal
W = sqrtflt(W,X,E(i),S,gamma,N);
end
subplot(2,1,1),plot(1:length(Y),Y*SF); title(\'Input Signal\');
subplot(2,1,2),plot(1:length(E),E*sf); title(\'Enhanced Signal\');
4) % program to illustrate adaptive filtering using the RLS algorithm:
% X delayed input signal
% Y measured signal
% W coefficient vector
% E enhanced signal
N = 30; % filter length
M = 1; % stages of delay
SF = 2048; % 12-bit ADC scaling
p0 = 0.05;
w0 = 100;
gamma = 0.98;
RemoveMean = 0; % 1 to remove the mean, 0 otherwise
W = w0*ones(N,1); % adaptive filter weights
X = zeros(N,1);
delay = zeros(1,M+1);
P = p0*diag(ones(1,N),0);
if w0==0
sf = SF; % scaling factor for display
else
sf = SF/N/w0;
end
in = fopen(\'ADF.dat\',\'r\'); %read input data from specified data file
Y = fscanf(in,\'%g\',inf)/SF;
fclose(in);
if RemoveMean % remove the mean from the data if required
Y = Y - sum(Y)/length(Y);
end
for i=1:length(Y)
if M>0
delay(2:M+1) = delay(1:M); % shift input data in delay registers
end
delay(1) = Y(i);
X(2:N) = X(1:N-1); % update buffer
X(1) = delay(M+1);
E(i) = Y(i) - X\'*W; % the enhanced signal
G = P*X/(gamma + X\'*P*X);
P = (P - G*X\'*P)/gamma;
W = W + G*E(i); % update the weights
end
subplot(2,1,1),plot(1:length(Y),Y*SF); title(\'Input Signal\');
subplot(2,1,2),plot(1:length(E),E*sf); title(\'Enhanced Signal\');
5) udu algorithm - a numerically stable form of the recursive least squares algorithm:
% inputs:
% x() input vector
% dn latest input data value
% w() coefficient vector
% u() vector containing elements of U and D
% outputs:
% en error signal
% yn digital filter output
% w() updated coefficient vector
% u() updated elements of U and D
sf = 1/gamma;
m=1; % update the UD elements
v=zeros(1,N);
v(1)=x(1);
for j=2:N
v(j)=x(j);
for k=1:j-1
m=m+1;
v(j)=v(j)+u(m)*x(k);
end
m=m+1;
b(j)=u(m)*v(j);
end
b(1)=u(1)*x(1);
alpha=gamma+b(1)*v(1);
delta=1/alpha;
u(1)=u(1)*delta;
m=1;
for j=2:N
beta1=alpha;
alpha=alpha+b(j)*v(j);
p=-v(j)*delta;
delta=1/alpha;
for k=1:j-1
m=m+1;
beta=u(m);
u(m)=beta+b(k)*p;
b(k)=b(k)+b(j)*beta;
end
m=m+1;
u(m)=u(m)*beta1*delta*sf;
end
perr=ek/alpha;
for j=1:N % update the weights
w(j)=w(j)+b(j)*perr;
end
