Q3) A periodic signal x(t) is given by x(t) = 1+ 3 cos(300rt) + 2sin (500t – -) A) Find the Fourier series coefficients of x(t). B) The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) + 2y(t) = x(t) dt Y(w) i) Determine the frequency response H(w) X(w) ii) If x(t) = e"u(t), determine Y(@), the Fourier tranform of the output. 111) Find y(t) for the input given above.

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Q3) A periodic signal x(t) is given by
x(t) = 1+ 3 cos(300rt) + 2sin (500t – -)
A) Find the Fourier series coefficients of x(t).
B) The output of a causal LTI system is related to the input x(t) by the differential
equation
dy(t)
+ 2y(t) = x(t)
dt
Y(w)
i) Determine the frequency response H(w)
X(w)
ii) If x(t) = e"u(t), determine Y(@), the Fourier tranform of the output.
111) Find y(t) for the input given above.
Transcribed Image Text:Q3) A periodic signal x(t) is given by x(t) = 1+ 3 cos(300rt) + 2sin (500t – -) A) Find the Fourier series coefficients of x(t). B) The output of a causal LTI system is related to the input x(t) by the differential equation dy(t) + 2y(t) = x(t) dt Y(w) i) Determine the frequency response H(w) X(w) ii) If x(t) = e"u(t), determine Y(@), the Fourier tranform of the output. 111) Find y(t) for the input given above.
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