Using the Fourier Transform
نویسنده
چکیده
We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give sufficient conditions for a shift problem to be solved efficiently by our algorithm. We also show that combining the shift problem with the hidden subgroup problem results in a hidden coset problem. This naturally captures the redundancy in the shift due to the periodic structure of multiplicative characters over Z/nZ.
منابع مشابه
Simulation of Singular Fourth- Order Partial Differential Equations Using the Fourier Transform Combined With Variational Iteration Method
In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...
متن کاملOn The Simulation of Partial Differential Equations Using the Hybrid of Fourier Transform and Homotopy Perturbation Method
In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...
متن کاملPathologies cardiac discrimination using the Fast Fourir Transform (FFT) The short time Fourier transforms (STFT) and the Wigner distribution (WD)
This paper is concerned with a synthesis study of the fast Fourier transform (FFT), the short time Fourier transform (STFT and the Wigner distribution (WD) in analysing the phonocardiogram signal (PCG) or heart cardiac sounds. The FFT (Fast Fourier Transform) can provide a basic understanding of the frequency contents of the heart sounds. The STFT is obtained by calculating the Fourier tran...
متن کاملResidual analysis using Fourier series transform in Fuzzy time series model
In this paper, we propose a new residual analysis method using Fourier series transform into fuzzy time series model for improving the forecasting performance. This hybrid model takes advantage of the high predictable power of fuzzy time series model and Fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...
متن کاملEquivalence of K-functionals and modulus of smoothness for fourier transform
In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.
متن کاملDetection of high impedance faults in distribution networks using Discrete Fourier Transform
In this paper, a new method for extracting dynamic properties for High Impedance Fault (HIF) detection using discrete Fourier transform (DFT) is proposed. Unlike conventional methods that use features extracted from data windows after fault to detect high impedance fault, in the proposed method, using the disturbance detection algorithm in the network, the normalized changes of the selected fea...
متن کامل