Final answer:
The input-output relationship of the LTI system is y(t) = 4x(t)cos(5t). Taking the Fourier transform of y(t) with the given input x(t), we can find Y(ω) to be 2π * sinc(ω/8-5).
Step-by-step explanation:
The input-output relationship of the LTI system can be represented as y(t) = 4x(t)cos(5t). Since the given input is x(t) = πSinc(8t), we can find Y(ω) by taking the Fourier transform of y(t) using the given input. Applying the Fourier transform, we get Y(ω) = 2π * sinc(ω/8-5). To sketch the graph of Y(ω), we can plot the function sinc(ω/8-5) with respect to ω.