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Question

# The output y(t) of a causal LTI system is related to the input x(t) as,dy(t)dt+2y(t)=x(t). If the frequency response of output is e−j2ω2+jω, then the value of x(t) at t=2 is

A
0.5
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B
4
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C
1
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D
2
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Solution

## The correct option is C 1Given, Causal LTI system, dy(t)dt+2y(t)=x(t) By using Fourier transform, jωY(ω)+2Y(ω)=X(ω) Y(ω)[2+jω]=X(ω) Y(ω)=X(ω)2+jω By comparing above equation with the given output frequency response. X(ω)=e−j2ω We know that, δ(t−t0)F.T⟷e−jωt0 δ(t−2)F.T⟷e−j2ω ∴x(t)=δ(t−2) at t=2;x(2)=δ(t−2)=δ(0)=1

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