Consider the continuous-time signal x(t). The Fourier transform of x(t) is X(j o

Question

Consider the continuous-time signal x(t). The Fourier transform of x(t) is X(j omega) = . Signal x(t) is sent to the input of a first system (System 1), obtaining the output signal y(t) = tx(t). Signal y(t) is then sent to the input of a second system (System 2), obtaining the output signal z(t) = dy(t)/dt. Derive, sketch and label carefully Z(j omega), defined as the Fourier transform of signal z(t) Demonstrate which one of the following claims is true z(t) = x(t) z(t) = x(-t) z(t) = dx(t)/dt z(t) = x(t - 1) z(t) = x(t + 1)

Explanation / Answer

2.z(t)=x(-t)

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