Related papers: Fast Inverse Nonlinear Fourier Transform
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…
By viewing the nonuniform discrete Fourier transform (NUDFT) as a perturbed version of a uniform discrete Fourier transform, we propose a fast, stable, and simple algorithm for computing the NUDFT that costs $\mathcal{O}(N\log…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
We explore the class of exponential integrators known as exponential time differencing (ETD) method in this letter to design low complexity nonlinear Fourier transform (NFT) algorithms that compute discrete approximations of the scattering…
We have developed an algorithm for transferring radiation in three-dimensional space. The algorithm computes radiation source and sink terms using the Fast Fourier Transform (FFT) method, based on a formulation in which the integral of any…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…
We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the…
In this paper, we study the impact of computational complexity on the throughput limits of the {\color{black}fast Fourier transform (FFT)} algorithm for {\color{black}orthogonal frequency division multiplexing(OFDM)} waveforms. Based on the…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
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…
We explore two classes of exponential integrators in this letter to design nonlinear Fourier transform (NFT) algorithms with a desired accuracy-complexity trade-off and a convergence order of $4$ on an equispaced grid. The integrating…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
Recently, a new polynomial basis over binary extension fields was proposed such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order $\mathcal{O}(n\lg(n))$, where $n$ is the number of points…
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
A simple least-squares optimisation enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an…
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…
An $\mathcal{O}(N(\log N)^2/\log\!\log N)$ algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev…
The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…
Non-line-of-Sight (NLOS) imaging systems collect light at a diffuse relay surface and input this measurement into computational algorithms that output a 3D volumetric reconstruction. These algorithms utilize the Fast Fourier Transform (FFT)…