Question

Determine the impulse response h(n) for the system described by the second-order

difference equation

y(n) - 4y(n - 1) + 4y(n - 2) = x(n) - x(n - 1)

Answer 1

The impulse response for the system described by the second-order difference equation is h(n) = (1/2)^n - (1/4)^n.

Step-by-step explanation:

The impulse response h(n) for the system described by the second-order difference equation can be found by setting all inputs to zero except for an input at time n = 0, which is set to 1.

Then, the system's output at time n = 0 is the value of the impulse response at that time.

By substituting x(n) = δ(n) and solving the difference equation, we find that the impulse response is given by:

h(n) = (1/2)^n - (1/4)^n