Journal ArticleDOI
DIFFT: A Fast and Accurate Algorithm for Fourier Transform Integrals of Discontinuous Functions
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TLDR
A new highly accurate fast algorithm is proposed by employing the analytical Fourier transforms of Gauss-Chebyshev-Lobatto interpolation polynomials and the scaled fast Fourier transform to achieve the exponential accuracy for evaluation of Fourier spectra at the whole frequency range with a low computational complexity.Abstract:
A new highly accurate fast algorithm is proposed for computing the Fourier transform integrals of discontinuous functions (DIFFT) by employing the analytical Fourier transforms of Gauss-Chebyshev-Lobatto interpolation polynomials and the scaled fast Fourier transform. This algorithm can achieve the exponential accuracy for evaluation of Fourier spectra at the whole frequency range with a low computational complexity. Furthermore, the algorithm allows the adaptive sampling densities for different sections of a piecewise smooth function. Numerical experiments are shown for the applications in computational electromagnetics.read more
Citations
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Journal ArticleDOI
A high accuracy conformal method for evaluating the discontinuous fourier transform
TL;DR: A highly accurate, fast algorithm is proposed to evaluate the flnite Fourier transform of both continuous and discontinues functions, which is not restricted by the Nyquist sampling theorem, thus avoiding the aliasing distortions that exist in other traditional methods.
Journal ArticleDOI
Discontinuous Fast Fourier Transform with Triangle Mesh for Two-dimensional Discontinuous Functions
TL;DR: This paper extends the discontinuous fast Fourier transform (DFFT) algorithm to deal with the two dimensional function with a discontinuous boundary of arbitrary shape and discretizes the support domain of the function by triangle mesh, which reduces the stair-casing error of an orthogonal grid required by FFT.
Journal ArticleDOI
An accurate conformal fourier transform method for 2d discontinuous functions
TL;DR: A highly accurate, fast conformal Fourier transform (CFT) algorithm is proposed to evaluate the flnite Fourier Transform of 2D discontinuous functions to take full advantages of high order interpolation and Gaussian quadrature methods to achieve highly accurate Fourier integration results with a low sampling density and small computation time.
Journal ArticleDOI
Quad-Based Fourier Transform for Efficient Diffraction Synthesis
TL;DR: This work proposes a technique based on a closed‐form solution of the continuous Fourier transform for simple vector primitives (quads) and proposes a hierarchical and progressive evaluation to achieve real‐time performance.
Journal ArticleDOI
WFRFT Secure Communication Method Based on Chaotic Parameter Pool
TL;DR: A random modulation order parameter pool is established by applying chaos technology and can greatly increase the bit error rate and processing time of unauthorized receivers, and a WFRFT secure communication method based on the chaotic parameter pool (CPP) is proposed.
References
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Journal ArticleDOI
The fractional Fourier transform and applications
TL;DR: The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing D FTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies.
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A fast, high-order quadrature sampled pre-corrected fast-fourier transform for electromagnetic scattering
TL;DR: It is shown that the QS‐PCFFT maintains high‐order convergence and scales as O(N) in memory and O( N log N) in floating point operations.
Journal ArticleDOI
Fast Fourier Transforms of Piecewise Constant Functions
TL;DR: The algorithm is based on the Lagrange interpolation formula and the Green's theorem, which are used to preprocess the data before applying the fast Fourier transform, and readily generalizes to higher dimensions and to piecewise smooth functions.
Journal ArticleDOI
Fast Fourier transform for discontinuous functions
Guo-Xin Fan,Qing Huo Liu +1 more
TL;DR: A fast algorithm for the evaluation of the Fourier transform of piecewise smooth functions with uniformly or nonuniformly sampled data by using a double interpolation procedure combined with the fast Fouriertransform (FFT) algorithm is presented.