In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us ...

In this article we will study the spectral properties of a deterministic signal exponentially damped in the past and in the future (the damping in the future is controlled by a time constant). The ...

Harmonic analysis occupies a central position in modern mathematical analysis by providing the tools to express complex functions as superpositions of simpler sinusoidal components via the Fourier ...

The Fourier transform underpins so much of our technological lives, in most cases probably without our realising it. The ability to mathematically split a waveform into its frequency components and ...

When it comes to mathematics, the average person can probably get through most of life well enough with just basic algebra. Some simple statistical concepts would be helpful, and a little calculus ...

A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its ...

Transactions of the American Mathematical Society, Vol. 272, No. 2 (Aug., 1982), pp. 785-802 (18 pages) The technique devised by Wong to derive the asymptotic expansions of multiple Fourier transforms ...