Question

If a system has the following impluse response :

h(t) = t * e^(2t) * Cos(t + π/4)

Write down its transfer function. What is the order of this system? Show all work.

Answer 1

To find the transfer function, take the Laplace transform of the impulse response. The transfer function is H(s) = sH(s-2) * COS(s + π/4). The order of the system is 1.

Step-by-step explanation:

The transfer function of a system can be determined by taking the Laplace transform of its impulse response. In this case, the impulse response is h(t) = t * e^(2t) * Cos(t + π/4).

To find the transfer function, we first take the Laplace transform of h(t):

L{h(t)} = L{t * e^(2t) * Cos(t + π/4)}

Using the time-shift property, we have:

L{e^(2t) * Cos(t + π/4)} = H(s-2) * COS(s + π/4)

So, the transfer function of the system is H(s) = L{h(t)} = sH(s-2) * COS(s + π/4).

The order of a system can be determined by counting the number of poles in the transfer function. In this case, the transfer function has one pole at s = 2, so the order of the system is 1.