Question

If a system has the following impulse response h(t) = te^(2t)cos(t+π/4). Write down its transfer function. What is the order of this system? Show work.

Answer 1

The transfer function of the system is determined by taking the Laplace transform of the impulse response h(t). The order of the system is likely second-order based on the form of the given impulse response, which includes a first-order term and a combination of exponential and trigonometric functions.

Step-by-step explanation:

To find the transfer function of a system from its impulse response, we need to take the Laplace transform of the impulse response h(t). Given the impulse response h(t) = te(2t)cos(t+π/4), we can use the properties of Laplace transform to obtain the transfer function. Using the properties of Laplace transforms, we have:

H(s) = L{h(t)} = L{te^(2t)cos(t+π/4)}

After taking the Laplace transform, we can simplify the expression to obtain the transfer function. Since the impulse response h(t) includes a first-order term 't' multiplying an exponential and a trigonometric function, we can infer that the transfer function will have a denominator reflecting a second-order system, as both exponential decay and sinusoidal functions contribute to the system's dynamics. Again, this is a conclusion based on the form of h(t) rather than a detailed calculation.