Related papers: Fast Computation of Partial Fourier Transforms
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…
This work presents a method of computing Voigt functions and their derivatives, to high accuracy, on a uniform grid. It is based on an adaptation of Fourier-transform based convolution. The relative error of the result decreases as the…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
We present a general diagrammatic approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra. This extends previous work wherein we derive best estimates for the computation of a Fourier…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…
In this work, we present the \emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the $N$-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an $N$-point…
Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering…
We consider the problem of building numerically stable algorithms for computing Discrete Fourier Transform (DFT) of $N$- length signals with known frequency support of size $k$. A typical algorithm, in this case, would involve solving…
We introduce a class of algorithms for constructing Fourier representations of Gaussian processes in $1$ dimension that are valid over ranges of hyperparameter values. The scaling and frequencies of the Fourier basis functions are evaluated…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
Energy evaluation using fast Fourier transforms enables sampling billions of putative complex structures and hence revolutionized rigid protein-protein docking. However, in current methods efficient acceleration is achieved only in either…
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…
Fast Fourier transform was included in the Top 10 Algorithms of 20th Century by Computing in Science & Engineering. In this paper, we provide a new simple derivation of both the discrete Fourier transform and fast Fourier transform by means…
In this paper, we consider a method for fast numerical computation of the Fourier transform of a slowly decaying function with given accuracy in given ranges of the frequency. In these decades, some useful formulas for the Fourier transform…
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…
We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector…