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Question 2014.S3.35: A differentiable non-constant even function x(t) has a deriv......

A differentiable non-constant even function x(t) has a derivative y(t), and their respective Fourier transforms are X(ω) and Y(ω). Which of the following statements is TRUE?

(a) X(ω) and Y(ω) are both real.

(b) X(ω) is real and Y(ω) is imaginary.

(c) X(ω) and Y(ω) are both imaginary.

(d) X(ω) is imaginary and Y(ω) is real.

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Given that y(t)={\frac{d}{d t}}\,x(t)

On Fourier transformation, Y(ω) = ωX(jω).
Therefore, X(ω) is real and Y(ω) is imaginary.

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