Question

I am calculating PT1 behavior in Matlab using the input vector u:

u(20:50,1) = 2;
k = 0.8;
x=zeros(50,1);
for i=2:size(u,1)
    x(i) = k*x(i-1) + (1-k)*u(i);
end

How can I remove the for loop to get the same result?

Answer 1

This is actually a first-order IIR filter, so you can use filter for that:

u(20:50, 1) = 2;
k = 0.8;
x = filter(1 - k, [1, -k], u);