A generalized Mobius transform, arithmetic Fourier transforms, and primitive roots

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A generalized Mobius transform, arithmetic Fourier transforms, and primitive roots

A general approach to arithmetic Fourier transforms is developed. The implementation is based on sine and cosine killer procedures pertaining to a generalized Möbius transform involving reduced periodic multiplicative arithmetical functions. It is shown that cosine killer procedures exist whenever one half of Euler’s totient function of the order of the transform is odd. Primitive roots and ind...

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A generalized Mobius transform and arithmetic Fourier transforms

A general approach to arithmetic Fourier transforms is developed. The implementation is based on the concept of killer polynomials and the solution of an arithmetic deconvolution problem pertaining to a generalized Mobius transform. This results in an extension of the Bruns procedure, valid for all prime numbers, and in an AFT that extracts directly the sine coefficients from the Fourier series.

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ژورنال

عنوان ژورنال: IEEE Transactions on Signal Processing

سال: 1996

ISSN: 1053-587X

DOI: 10.1109/78.502351