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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fourier analysis on finite abelian groups and the uncertainty principles
有限阿贝尔群 傅里叶分析 不确定性原理
2023/4/18
Let G be a finite abelian group. If f: G → C is a nonzero function with Fourier transform f , the Donoho-Stark uncertainty principle states that|supp(f)||supp(f )|≥|G|. The purpose of this talk is two...
西安电子科技大学数字信号处理英文课件Chapter5 The Discrete Fourier Transform
西安电子科技大学 数字信号处理 英文课件 Chapter5 Discrete Fourier Transform
2020/6/22
西安电子科技大学数字信号处理英文课件Chapter5 The Discrete Fourier Transform。
复旦大学数学物理方法课件第七章 Fourier变换。
复旦大学数学物理方法课件 Fourier变换和色散关系
复旦大学 数学物理方法 课件 Fourier变换和色散关系
2019/3/21
复旦大学数学物理方法课件 Fourier变换和色散关系。
青岛理工大学理学院复变函数与积分变换课件 Fourier变换的性质。
青岛理工大学理学院复变函数与积分变换课件 Fourier变换。
UNIMODULAR FOURIER MULTIPLIERS FOR MODULATION SPACES
Fourier multiplier modulation space short-time Fourier transform Schrodinger equation wave equation conservation of energy
2015/12/10
We investigate the boundedness of unimodular Fourier multipliers on modulation spaces. Surprisingly, the multipliers with general symbol ei|ξ|α, where α ∈ [0, 2], are bounded on all modulation spaces,...
Stability Theorems for Fourier Frames and Wavelet Riesz Bases
Frames Riesz basis nonharmonic series wavelets
2015/9/29
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type co...
SPARSE FOURIER TRANSFORM VIA BUTTERFLY ALGORITHM
Fourier transform butterfly algorithm multiscale methods far field pattern
2015/7/14
This paper introduces a fast algorithm for computing sparse Fourier transforms with spatial and Fourier data supported on curves or surfaces. This problem appears naturally in several important applic...
A FAST BUTTERFLY ALGORITHM FOR THE COMPUTATION OF FOURIER INTEGRAL OPERATORS
Fourier integral operators butterfly algorithm dyadic partitioning Lagrange interpolation separated representation multiscale computations
2015/7/14
This paper is concerned with the fast computation of Fourier integral operators of the general form Rd e2πıΦ(x,k)f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a st...
FAST COMPUTATION OF PARTIAL FOURIER TRANSFORMS
fast Fourier transform multiscale decomposition butterfly algorithm fractional Fourier transform wave extrapolation
2015/7/14
This paper is concerned with the evaluation of the partial Fourier transform ux =|k|ure in ...
FAST COMPUTATION OF FOURIER INTEGRAL OPERATORS
Fourier integral operators generalized Radon transform separated representation nonuniform fast Fourier transform matrix approximation operator compression randomized algorithms reflection seismology
2015/7/14
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation, general hyperbolic equations, an...
FAST WAVE COMPUTATION VIA FOURIER INTEGRAL OPERATORS
Wave equations Fourier integral operators discrete symbol calculus random sampling separated approximation multiscale computations
2015/7/14
This paper presents a numerical method for “time upscaling” wave equations, i.e., performing time steps not limited by the Courant-FriedrichsLewy (CFL) condition. The proposed method leverages recent ...
Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation in the acoustic approximation
Numerical solutions Body waves Seismic anisotropy Computational seismology Wave propagation Acoustic properties
2015/7/14
We introduce a novel finite-difference (FD) approach for seismic wave extrapolation in time.We derive the coefficients of the finite-difference operator from a lowrank approximation of the space-waven...