Problem 5.4 Find an explicit time domain expression for the output y(t) when the signal r(t) is passed through an LTI system with impulse response h(t) = sinc(12t - 4) for the following two scenarios: (a)x(t) = 3 cos(60πt+)-4 sin(70nt + 7) - 2. (b) r(t) = sinc(3t)sinc(4t).

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please have a step by step solution with the full answer. as of right now, I am confused on whether to use the dirac delta function to convert the cos and sin within x(t). what do i do with the shifts of pi/4 and pi/3? i know that the cosx= 2(δ(f−f0​)+δ(f+f0​)).

Problem 5.4 Find an explicit time domain expression for the output y(t) when the signal r(t)
is passed through an LTI system with impulse response h(t) = sinc(12t - 4) for the following
two scenarios:
(a)x(t) = 3 cos (60πt+)-4 sin(70nt + 1) - 2.
(b) r(t) =sinc(3t)sinc(4t).
Transcribed Image Text:Problem 5.4 Find an explicit time domain expression for the output y(t) when the signal r(t) is passed through an LTI system with impulse response h(t) = sinc(12t - 4) for the following two scenarios: (a)x(t) = 3 cos (60πt+)-4 sin(70nt + 1) - 2. (b) r(t) =sinc(3t)sinc(4t).
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