Signals and Systems - Fourier Transform

Let $X(\omega)$ be the Fourier transform of the signal $x(t) = e^{-t^4} \cos t$, $-\infty < t < \infty$. The value of the derivative of $X(\omega)$ at $\omega=0$ is ________ (rounded off to 1 decimal place).

The Fourier transform X($\omega$) of the signal x(t) is given by $X(\omega) = 1$, for $|\omega| W_0$ Which one of the following statements is true?

The Fourier transform of a continuous-time signal x(t) is given by X(ω) = 1 / (10+jω)^2, -∞ < ω < ∞, where j=√-1 and ω denotes frequency. Then the value of |ln x(t)| at t =1 is ________ (up to 1 decimal place). (ln denot...