Question

The signals for which Fourier transform does not exists is/are

• A. t u(t)
• B. $e^{2t}u\left(t\right)$
• C. sgn (t)
• D. 1

Answer 1

Answer: (A), (B)

$e^{2t}u\left(t\right)$

$sgnt\stackrel{F.T}{⟷}\frac{2}{j\omega }$

$1\stackrel{F.T}{⟷}2\pi \delta \left(\omega \right)$

both $e^{2t}$ u(t), t u(t) are unbounded signals. Therefore, Fourier transform does not exists.