ISSN:
1572-9125
Keywords:
65T05
;
42A99
;
Fourier coefficients
;
arithmetic Fourier Transform
;
Möbius function
;
summability by primes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The Arithmetic Fourier Transform (AFT) is an algorithm for the computation of Fourier coefficients, which is suitable for parallel processing and in which there are no multiplications by complex exponentials. This is accomplished by the use of the Möbius function and Möbius inversion. However, the algorithm does require the evaluation of the function at an array of irregularly spaced points. In the case that the function has been sampled at regularly spaced points, interpolation is used at the intermediate points of the array. Generally theAFT is most effective when used to calculate the Fourier cosine coefficients of an even function. In this paper a summability method is used to derive a modification of theAFT algorithm. The proof of the modification is quite independent of theAFT itself and involves a summation by primes. One advantage of the new algorithm is that with a suitable sampling scheme low order Fourier coefficients may be calculated without interpolation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01955877
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