The Fourier transform of a function x(t) is X(f). The Fourier transform of $${{dx(t)} \over {dt}}$$ will be

The amplitude spectrum of a Gaussian pulse is

The function f(t) has the Fourier Transform g($$\omega $$). The Fourier Transform of $$$g(t) = \left( {\int\limits_{ - \infty }^\infty {g(t){e^{ - j\omega t}}} } \right)\,is$$$

The Fourier transform of a real valued time signal has