The Bomem DA3 is a type of Fourier transform spectrometer used for measuring various spectral data and [Usagi Electric] has one. On his quest to understand it he runs down a number of rabbit holes, ...

A differentiable fractional Fourier transform (FRFT) implementation with layers that can be trained end-to-end with the rest of the network. This package provides implementations of both fast ...

ABSTRACT: The exponential transform or modified Fourier transform is an integral transform where the Kernel function is K a ( ξ,t )= a −iξt , and a∈] 1,+∞ [ . This is a general case of the Fourier ...

Fourier transform is a key method for analyzing signals in both time and frequency domains. The FFT is a computational algorithm that efficiently computes the discrete Fourier transform (DFT) and its ...

Abstract: In this paper, we define the Windowed Octonion Quadratic Phase Fourier Transform (WOQPFT) and derive its inversion formula, including its essential properties, such as linearity, ...

Abstract: The fractional Fourier transform (FRFT) parametrically generalizes the Fourier transform (FT) by a transform order, representing signals in intermediate time-frequency domains. The FRFT has ...

In the age of information overload, it can be troublesome to go through painstakingly long PDFs or when time is of the essence. With the ever-growing state of LLMs, skimming through a PDF has been ...

The sampling process of a signal is of an ideal type as it extends from −∞ to +∞ on the time axis, hence the infinite number of instants t n. This destroys the possibility of using an electronic ...

The so-called unit impulse (or mathematical impulse) is of considerable importance in signal theory. This tutorial will examine its physical meaning through an ideal experiment. Note that the delta ...