Question

The system function of a causal LTI system is:

H(s) = s+1/s²+2s+2
Determine and sketch the response y(t) when the input is:
x(t)=e⁻|ᵗ|, -[infinity] < t < [infinity]

Answer 1

The system function H(s) = (s+1)/(s^2+2s+2) can be used to determine the response y(t) when the input is x(t) = e^(-|t|) by finding the inverse Laplace transform of H(s) and convolving it with the input signal.

Step-by-step explanation:

The system function of a causal LTI system is given by H(s) = (s+1)/(s^2+2s+2). To determine the response y(t) when the input is x(t) = e^(-|t|), we need to find the inverse Laplace transform of H(s) and then convolve it with the input signal x(t). Let's first find the inverse Laplace transform of H(s):

H(s) = (s+1)/(s^2+2s+2)

To find the inverse Laplace transform, we can use partial fraction decomposition:

H(s) = (s+1)/(s^2+2s+2) = A/(s+1) + (Bs+C)/(s^2+2s+2)