Related papers: Illuminating Fourier Series with Audacity
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
The sensory perceptions of vision and sound may be considered as complementary doorways towards interpreting and understanding physical phenomena. We provide a few selected samples where scientific data of systems usually not directly…
This proposal presents a methodology called enriched three-tier test, based on a similar test previously discussed in the literature. Ours consists of the use of justification and degrees of confidence combined with a multiple-choice test.…
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…
We use probability urn models to discover some known and unknown series identities involving Fibonacci numbers.
We propose an efficient method for rendering complex luminaires using a high-quality octree-based representation of the luminaire emission. Complex luminaires are a particularly challenging problem in rendering, due to their caustic light…
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…
Contrary to geometric acoustics-based simulations where the spatial information is available in a tangible form, it is not straightforward to auralize wave-based simulations. A variety of methods have been proposed that compute the ear…
An estimated 253 million people have visual impairments. These visual impairments affect everyday lives, and limit their understanding of the outside world. This can pose a risk to health from falling or collisions. We propose a solution to…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
The present paper presents two new approaches to Fourier series and spectral analysis of singular measures.
This note gives a summary of ideas concerning Applied Fourier Analysis, mostly formulated for those who have to give such courses to engineers or mathematicians interested in real life applications. It tries to answer recurrent questions…
There have been many papers with algorithms for improving fairness of machine-learning classifiers for tabular data. Unfortunately, most use only very few datasets for their experimental evaluation. We introduce a suite of functions for…
There have been several modifications of how basic calculus has been taught, but very few of these modifications have considered the computational tools available at our disposal. Here, we present a few tools that are easy to develop and…
Fourier transform spectroscopy (FTS) has been widely used as an analytical tool for many applications in science and engineering. In this paper, we describe the operation principle and practical implementation of an FTS prototype. First,…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…
The analysis of signals created by a variety of instruments involves calculating the phase of a sinusoidal type signal. One widely used method to extract this information is through the use of Fourier transforms, but it is known that…
In this paper, we present a new Light Field representation for efficient Light Field processing and rendering called Fourier Disparity Layers (FDL). The proposed FDL representation samples the Light Field in the depth (or equivalently the…
In undergraduate optics courses, diffraction gratings are studied extensively, generally within the scalar approximation. When the vector nature of light is taken into account, so-called polarization diffraction gratings have been proposed,…
In this work, we propose using camera arrays coupled with coherent illumination as an effective method of improving spatial resolution in long distance images by a factor of ten and beyond. Recent advances in ptychography have demonstrated…