Introduction

Every object described by a function f of a real variable gives rise to a “spectral” image described by the function (1)$$\hat{f}\left( \xi \right): = \frac{1}{{2\pi }}\int_{{ - \infty }}^{\infty } {f\left( t \right){{e}^{{ - it\xi }}}dt\quad \left( {\xi \in \mathbb{R}} \right).} $$ The right side makes sense for every ξ ∈ ℝ if f ∈ L1(ℝ). The function f̂ is called the Fourier transform of f. (Sometimes we write F(f) instead of f̂). The Fourier transform can be defined not only for a summable function but also for any tempered distribution.