Given a Fourier transform pair x(t) ↔ X(jω) = \(\frac{2 sinω}{ω}\), where, x(t) = 1 for |t|<1 and 0, otherwise. Then the Fourier transform of y(t) having the shape of a triangular waveform from t=-2 to t=2 and maximum peak value=2 is ___________

(a) \(\frac{4 sin^2 ω}{ω^2}\)

(b) \(\frac{2 sin^2 ω}{πω^2}\)

(c) \(\frac{8π sin^2 ω}{ω^2}\)

(d) \(\frac{8 sin^2 ω}{ω^2}\)

This question was posed to me in examination.

This intriguing question originated from Characterization and Nature of Systems topic in chapter Laplace Transform and System Design of Signals and Systems