Question

The Inverse Fourier transform  of the signal 2πδ(ω) + πδ(ω-4π) + πδ(ω+4π) is ______________

(a) 2π(1 – cos 4πt)

(b) π (1 – cos 4πt)

(c) 1 + cos 4πt

(d) 2 π (1 + cos 4πt)

The question was posed to me in an online interview.

The above asked question is from Common Fourier Transforms topic in chapter Fourier Transform of Signals and Systems

Answer 1

Right choice is (c) 1 + cos 4πt

Best explanation: x (t) = \(\frac{1}{2π} \int_{-∞}^∞\) [2πδ(ω) + πδ(ω-4π) + πδ(ω+4π)] e^jωt dω

= 1 + \(\frac{1}{2} e^{j4πt} +  \frac{1}{2} e^{-j4πt}\)

= 1 + cos 4π