% SMOOTHER.M A smoothing filter defined as
%   y(n) = a*y(n-1) +(1-a)*x(n) , y(-1)=0
%   x(n) is input signal, y(n) is smoothed output
%
% Test signal is sin(w*t) with random noise 
%  INPUT:  Weighing factor a
%  OUTPUT: Plot of x and y
%
clear, clf
w=2*pi/5;
t = linspace(0,10,100);     % Time steps
s = sin(w*t);               % Noiseless signal
% Add random noise
len=size(t);
na = 0.1;                   % Noise amplitude
noise = na*(rand(len)-.5);	 % (-.05 to +.05)
x = s + noise;
%
% Weighing factor
a = input('Weighing factor a= ')
%
y(1)=(1-a)*x(1);
for I=2:100
 y(I) = a*y(I-1) + (1-a)*x(I);  % Digital Filter
end
plot(t,x,t,y)
xlabel('Time'), ylabel('Signals')
title(['Effect of Smoothing Filter, a = ', num2str(a)])
legend('Input x','Output y')