In this paper we define the convolution of functionals on abstract Wiener space and establish the relationship between the Fourier-Wiener transforms of each functional and the Fourier-Wiener transform ...

Comprehensive introduction to analysis of continuous and discrete-time signals and systems. Linear time-invariant systems, convolution; Fourier series representations of periodic signals; Continuous ...

As shown in the last subsection, kernel density estimates can be expressed as a submatrix of a certain convolution. The fast Fourier transform (FFT) is a computationally effective method for computing ...

pJTC Convolutional techniques. (a) Comparison of spatial convolution, Fourier electrical convolution, and Fourier optical convolution in terms of computational complexity. (b) Schematic of a JTC, ...

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, ...