Related papers: Efficiently Computing Sparse Fourier Transforms of…
Farey sequence has been a topic of interest to the mathematicians since the very beginning of last century. With the emergence of various algorithms involving the digital plane in recent times, several interesting works related with 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…
We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not…
Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…
The special affine Fourier transform (SAFT) is a promising tool for analyzing non-stationary signals with more degrees of freedom. However, the SAFT fails in obtaining the local features of non-transient signals due to its global kernel and…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
This paper introduces a quantum-inspired denoising framework that integrates the Quantum Fourier Transform (QFT) into classical audio enhancement pipelines. Unlike conventional Fast Fourier Transform (FFT) based methods, QFT provides a…
The singular values of convolutional mappings encode interesting spectral properties, which can be used, e.g., to improve generalization and robustness of convolutional neural networks as well as to facilitate model compression. However,…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
The complexity of computing the Fourier transform is a longstanding open problem. Very recently, Ailon (2013, 2014, 2015) showed in a collection of papers that, roughly speaking, a speedup of the Fourier transform computation implies…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
Since the evolution of digital computers, the storage of data has always been in terms of discrete bits that can store values of either 1 or 0. Hence, all computer programs (such as MATLAB), convert any input continuous signal into a…
In this work, we propose an algorithm for a filter based on the Fast Fourier Transform (FFT), which, due to its characteristics, allows for an efficient computational implementation, ease of use, and minimizes amplitude variation in the…
Multi-dimensional Fourier transforms are key mathematical building blocks that appear in a wide range of applications from materials science, physics, chemistry and even machine learning. Over the past years, a multitude of software…
Span programs characterize the quantum query complexity of binary functions $f:\{0,\ldots,\ell\}^n \to \{0,1\}$ up to a constant factor. In this paper we generalize the notion of span programs for functions with non-binary input/output…
In this work, we consider a new type of Fourier-like representation of Boolean function $f\colon\{+1,-1\}^n\to\{+1,-1\}$ \[ f(x) = \cos\left(\pi\sum_{S\subseteq[n]}\phi_S \prod_{i\in S} x_i\right). \] This representation, which we call the…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
Decomposing a flow on a Directed Acyclic Graph (DAG) into a weighted sum of a small number of paths is an essential task in operations research and bioinformatics. This problem, referred to as Sparse Flow Decomposition (SFD), has gained…
Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a Hidden Subgroup problem, in which an unknown subgroup H of a group G must be determined from a uniform superposition on a…