%--------------------------- Begin Lab 4 --------------------
% Colin Joye
% ECE 3770-01
% Lab 4, Linear Adaptive Prediction
% due 3/01
% run 'c:\my documents\elec\neural'
clear;

wk = 0;   % Weights for predictor.
x  = 0;   % Signal being predicted.

u = 0.01;       % Optimization step size.
leng = 4;       % length of the filter.
lrate = u/leng; % learning rate (real), 0< lrate <1.0

%wk[n]=wk[n-1]+u*x[n-k]*e[n]; % Weight calculation.
%e[n]=x[n]-sum(wk[n]*x[n-m]); % Error calculation.

% "time" defines the time steps of the simulation.
time = 1:2000;
%time=1:0.01:3.5;

% X is a noisy signal, with SNR=20dB.
%X=sin((time/80).^1.6)+wgn(1,length(time),-20);  
X = [sin(time(1:1220)/50) sin(time(1221:end)/15)]+wgn(1,length(time),-20);  
%X=sin(sin(time).*time*10);

% P is the signal over these steps.
P = con2seq(X);

% T is a signal derived from P by shifting it to the 
% left, multiplying it by 2, and adding it to itself.
T = con2seq(2*[0 X(1:(end-1))]+X);

% plotting the two signals.
figure(1)
subplot(211);
plot(time,cat(2,P{:}),time,cat(2,T{:}),[1 length(time)],[0 0],'k');
title('Input and Target Signals');
xlabel('Time');
ylabel('Input (blue), Target (green)');

% The linear network must have tapped delay in order to 
% learn the time-shifted correlation between P and T: 
% "newlin" creates a linear layer.
net = newlin([-3 3],1,[0 1],lrate);
% [-3 3] is the expected input range.
% second argument is the number of neurons in the layer.
% [0 1] specifies one input with no delay and one input 
% with a delay of one.
% The last argument is the learning rate.

% "Adapt" simulates adaptive networks.  It takes a network, a 
% signal, and a target signal, and filters the signal adaptively.
[net,Y,E,Pf] = adapt(net,P,T);
figure(1)
subplot(212);
plot(time,cat(2,Y{:}),'b',time,cat(2,T{:}),'r',time,cat(2,E{:}),'g',[1 length(time)],[0 0],'k');
xlabel('Time');
ylabel('Input (red), Target (blue), Error (green)');

%--------------------------- End Lab 4 --------------------