Calculate Step Impulse Response: y(n) = a*y(n-1) + K*b*x(n-1)+K*x(n)

[cutesteph]

y(n) = a * y(n-1) + K * b * x(n-1) + K * x(n), where |a| < 1.

(a) Calculate its impulse response, h(n).
the homogenous equation is l^n-1(l-a) = 0 => 1 = a
so h(n) = [ka^n ] u(n)

(b) Calculate its step response.


I can't seem to find any examples online and my book says nothing about step responses. I am not sure where to start.

 

[rbj]

1. learn to use \LaTeX here.
2. looks like homework.
3. except for x[0], if all other x[n] is zero, what would y[n] look like? (that might give you a hint about what h[n] might be.)
4. integrate h[n] to get the step response.