Question

If the FT of x(t) is \(\frac{2}{ω}\) sin⁡(πω), then the FT of e^j5t x(t) is ____________

(a) \(\frac{2}{ω-5}\) sin⁡(πω)

(b) \(\frac{2}{ω+5}\) sin⁡{π(ω-5)}

(c) \(\frac{2}{ω+5}\) sin⁡(πω)

(d) \(\frac{2}{ω-5}\) sin⁡{π(ω-5)}

The question was asked in a job interview.

I want to ask this question from Trigonometric Fourier Series topic in chapter Fourier Series of Signals and Systems

Answer 1

The correct option is (d) \(\frac{2}{ω-5}\) sin⁡{π(ω-5)}

Explanation: Given that the FT of x (t) is \(\frac{2}{ω}\) sin⁡(πω)

Applying time shifting and scaling property, we get the FT of e^j5t x (t) as \(\frac{2}{ω-5}\) sin⁡{π(ω-5)}.