EKF_Signal Processing.m

clc; 
clear all; 
close all; 
[x fs]=audioread('/Users/AvnishSachar/Downloads/WienerNoiseReduction/sp01_train_sn10.wav'); 
sound(x,fs);
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; 
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');