Question: 1). Consider an LTI system whose response to the input x(t)=[e t +e 3t ]u(t) is $$y(t)=[2e^{-t}-2e^{-4t}]u(t). (a) Find the frequency response of this system.

1). Consider an LTI system whose response to the input

x(t)=[e−t+e−3t]u(t)

is $$y(t)=[2e^{-t}-2e^{-4t}]u(t). 

(a) Find the frequency response of this system. 

(b) Determine the system's impulse response. 

(c) Find the deferential equation relating the input and the output of the system.

2). Determine the output sequence y[n] for x[n] using Z Domain technique.

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