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 ...

In this paper we describe a method for computing the Discrete Fourier Transform (DFT) of a sequence of $n$ elements over a finite field $\mathrm{GF}(p^m)$ with a ...

The linear canonical transform (LCT) is a versatile integral transform that generalises classical transforms such as the Fourier, fractional Fourier, and Fresnel transforms. By utilising four ...

This article presents two important DSP techniques, the overlap-add method, and FFT convolution. The overlap-add method is used to break long signals into smaller segments for easier processing. FFT ...

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, ...