A fast FFT-based discrete Legendre transform
نویسندگان
چکیده
منابع مشابه
A fast FFT-based discrete Legendre transform
An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...
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The DFT can be reduced from exponential time with the Fast Fourier Transform algorithm. Fast Fourier Transform (FFT) One wonders if the DFT can be computed faster: Does another computational procedure an algorithm exist that can compute the same quantity, but more e ciently. We could seek methods that reduce the constant of proportionality, but do not change the DFT's complexity O ( N ) . Here,...
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basically saying we care not about the rest of x[n], since it is zero. Pretend that it is periodic for analysis purpose since for the DFT it makes no difference. Defined only for 0≤ n,k ≤ N−1. The rest is zero. This means the inherent periodicity is not represented. Notation x[n] DFT ←→ X [k] Lots of properties (similar to DFS) circular convolution is important. Given x1[n] and x2[n], form x̃1[n...
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ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2015
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drv060