clc;
clear all;
close all;
load handel.mat
filename = 'handel.wav';
[x, fs]=audioread('handel.wav');
v=rand (size(x)); % adding a random Gaussian noise eqn
orig=x+v; % noisy speech signal
no=orig;
N=length(x); % length of the input signal
F = zeros (5, N); % initialization of standard transition matrix
I = eye (5); % transition matrix
H = zeros (5,N);
sig = zeros (5, 5*N); % priori or posteri covariance matrix.
K = zeros (5, N); % kalman gain.
XX = zeros (5, N); % kalman coefficient for yy.
y = zeros (1, N); % requiring signal (desired signal)
vv = zeros (1, N); % predicted state error vector
yy = zeros (1, N); % Estimated error sequence
Q = 0.0001*eye (5, 5); % Process Noise Covariance.
R = 0.1; % Measurement Noise Covariance
y=x (1: N); % y is the output signal produced.
sig (1:5, 1:5) = 0.1*I;
for k=6: N
F(1:5,k)=-[y(k-1);y(k-2);y(k-3);y(k-4);y(k-5)];
H(1:5,k)=-[yy(k-1);yy(k-2);yy(k-3);yy(k-4);yy(k-5)];
K(1:5,k)=sig(1:5,5*k-29:5*k-25)*F(1:5,k)*inv(F(1:5,k)'*sig(1:5,5*k-29:5*k-25)*F(1:5,k)+R); %Kalman Gain
sig(1:5,5*k-24:5*k-20)=sig(1:5,5*k-29:5*k-25)-sig(1:5,5*k-29:5*k-25)*F(1:5,k)*inv(F(1:5,k)'*sig(1:5,5*k-29:5*k-25)*F(1:5,k) +R)*(F(1:5,k)'*sig(1:5,5*k-29:5*k-25))+Q; % error covariance matrix
XX(1:5,k) =(I - K(1:5,k)*F(1:5,k)')*XX(1:5,k-1) + (K(1:5,k)*y(k)); % posteriori value of estimate X(k)
orig (k) =y (k)-(F (1:3, k)'*XX (1:3, k)); % estimated speech signal
yy (k) = (H (1:5, k)'*XX (1:5, k)) + orig (k); % no. of coefficients per iteration
end;
for it = 1:1: length(x)
MSE (it) = orig (it) - x (it);
end;
sound(x,fs )
pause(size(x,1)/fs);
sound(no,fs)
pause(size(no,1)/fs);
sound(orig,fs)
% pause(size(y1,1)/fs);
sound(x,fs )
tt = 1:1: length(x);
figure (1); subplot (311); plot(x); title ('ORIGINAL SIGNAL');
subplot (312); plot (no); title ('Noisy Speech Signal');
subplot (313); plot (orig); title ('ESTIMATED SIGNAL');
figure (2); plot (tt, x, tt, orig); title ('Combined plot'); legend ('original’,’ estimated');
figure (3); plot (MSE.^2); title ('Mean square error');