Question

The unit response of an LTIC system is h(t)=(10e−³ᵗ −e−ᵗ) u(t). Find this system's (zero-state) response y(t)(=h(t)∗x(t)) if the input x(t) is

(a) 4u(t)
(b) 3e⁻²ᵗ u(t)
(c) (e⁻²ᵗ−e⁴ᵗ)u(t)

Answer 1

The zero-state response y(t) for different input functions x(t) can be found by substituting the input functions into the response equation and performing the convolution.

Step-by-step explanation:

The unit response of an LTIC system is represented by h(t) = (10e^(-3t) - e^(-t))u(t). To find the zero-state response y(t) (which is h(t) * x(t)) for different inputs x(t), we simply substitute the given input functions into the response equation and perform the convolution.

(a) y(t) = h(t) * x(t) = (10e^(-3t) - e^(-t))*4

(b) y(t) = h(t) * x(t) = (10e^(-3t) - e^(-t))*(3e^(-2t))

(c) y(t) = h(t) * x(t) = (10e^(-3t) - e^(-t))*(e^(-2t)-e^(4t))