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Fourier analysis and signal processing by use of the Möbius inversion formula. (English) Zbl 0701.94001
Summary: In this paper, a new Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number- theoretic method of the Möbius inversion of series. The Fourier transform method developed in this paper is shown also to yield the convolution of two signals. A computer simulation shows that this method to find Fourier coefficients is quite suitable for digital signal processing. Also, it competes with the classical FFT approach in terms of accuracy, complexity, and speed.
MSC:
94A11Application of orthogonal and other special functions in communication
94A12Signal theory (characterization, reconstruction, filtering, etc.)
65T50Discrete and fast Fourier transforms (numerical methods)