Question

Roughly sketch both the input and the output.

Consider an LTI system whose response to the input
x(t) = [e + e⁻³ᵗ]u(t)
is
y(t)= [2e⁻ᵗ-2e⁻⁴ᵗ ]u(t).
(a) Find the frequency response of this system.

Answer 1

To find the frequency response of the given LTI system, we need to determine the system's response to different frequency components in the input signal.

Step-by-step explanation:

The response to the given input, x(t) = [e + e⁻³ᵗ]u(t), is y(t) = [2e⁻ᵗ-2e⁻⁴ᵗ ]u(t).

To find the frequency response of this system, we need to determine how the system responds to different frequency components in the input signal.

In this case, the frequency response can be found by taking the Fourier transform of the impulse response, which is the output of the system when the input is an impulse function.