Related papers: A new Truncated Fourier Transform algorithm
Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and…
A novel template matching algorithm that can incorporate the concept of deformable parts, is presented in this paper. Unlike the deformable part model (DPM) employed in object recognition, the proposed template-matching approach called…
In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a…
Fourier and related transforms is a family of algorithms widely employed in diverse areas of computational science, notoriously difficult to scale on high-performance parallel computers with large number of processing elements (cores). This…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
With the growing demand for non-Euclidean data analysis, graph signal processing (GSP) has gained significant attention for its capability to handle complex time-varying data. This paper introduces a novel sampling method based on the joint…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
We study the intrinsic transformation of feature maps across convolutional network layers with explicit top-down control. To this end, we develop top-down feature transformer (TFT), under controllable parameters, that are able to account…
Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the…
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $\R^n$, that generalizes the $n$-th fold DFT of the integer lattice $\Z^n$ to arbitrary lattices. This definition is not applicable for…
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…
We explore a new form of DFT, which we call the Polynomial Transform. It functions over finite fields, and a size $n$ transform takes $O(n)$ operations. In the multitape Turing machine model, it allows us to multiply two $n$ bit numbers in…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a…
We provide faster randomized algorithms for computing an $\epsilon$-optimal policy in a discounted Markov decision process with $A_{\text{tot}}$-state-action pairs, bounded rewards, and discount factor $\gamma$. We provide an…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…