Numerical implementation of Fourier transforms and associated problems
نویسندگان
چکیده
منابع مشابه
Numerical stability of nonequispaced fast Fourier transforms
This paper presents some new results on numerical stability for multivariate fast Fourier transform of nonequispaced data (NFFT). In contrast to fast Fourier transform (of equispaced data), the NFFT is an approximate algorithm. In a worst case study, we show that both approximation error and roundoff error have a strong influence on the numerical stability of NFFT. Numerical tests confirm the t...
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Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importanc...
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It is often the case that an operation originally defined for integer orders can be generalized to fractional or even complex orders in a meaningful and useful way. A basic example is the power operation. The ath power of x, denoted by Xa, might be defined as the number obtained by multiplying unity a times with x. Thus X = X X X X X. This definition makes sense only when a is an integer. Howev...
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The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized spatial filtering systems: Several filters...
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Recently, it has been proved that a Fourier transform for the symmetric group S„ based on Young's seminormal form can be evaluated in less than 0.5(h3 + n2)n\ arithmetic operations. We look at this algorithm in more detail and show that it allows an efficient software implementation using appropriate data structures. We also describe a similarly efficient algorithm for the inverse Fourier trans...
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ژورنال
عنوان ژورنال: International Journal of Multidisciplinary Studies
سال: 2014
ISSN: 2465-6380,2362-079X
DOI: 10.4038/ijms.v1i1.27