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 ...

Let f(u) be the Fourier-Stieltjes transform of a real or complex-valued function F(α) of bounded variation on (— ∞, ∞). It is shown that if f(u) belongs to L2 on an interval of infinite range, then ...

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 ...

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 ...

Perhaps the most beautiful aspect of mathematics is that it applies to literally everything, even things that do not exist in ...