Adaptive Noise Cancellation

A linear neuron is allowed to adapt so that given one signal, it can predict a second signal.

TIME defines the time steps of this simulation. P defines a signal over these time steps. T is a signal derived from P by shifting it to the left, multiplying it by 2 and adding it to itself.

time = 1:0.01:2.5;
X = sin(sin(time).*time*10);
P = con2seq(X);
T = con2seq(2*[0 X(1:(end-1))] + X);

Here is how the two signals are plotted:

plot(time,cat(2,P{:}),time,cat(2,T{:}),'--')
title('Input and Target Signals')
xlabel('Time')
legend({'Input','Target'})

The linear network must have tapped delay in order to learn the time-shifted correlation between P and T. The linearlayer function creates a linear layer. [0 1] specifies one input with no delay and one input with a delay of one. The last argument is the learning rate.

net = linearlayer([0 1], 0.1);

ADAPT simulates adaptive networks. It takes a network, a signal, and a target signal, and filters the signal adaptively. Plot the output Y in blue, the target T in red and the error E in green. By t=2 the network has learned the relationship between the input and the target and the error drops to near zero.

[net,Y,E,Pf]=adapt(net,P,T);
plot(time,cat(2,Y{:}),'b', ...
   time,cat(2,T{:}),'r', ...
   time,cat(2,E{:}),'g',[1 2.5],[0 0],'k')
legend({'Output','Target','Error'})