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A sampling formula in signal processing and the prime number theorem. (English) Zbl 0858.65147
Summary: An algorithm known as the arithmetic Fourier transform, which is used in the computation of Fourier coefficients, is shown to be related to the Prime Number Theorem. The algorithm turns out to be applicable to step functions and so can be applied to a phase filter related to the Buys-Ballot filter.
MSC:
65T50 Numerical methods for discrete and fast Fourier transforms
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
11A25 Arithmetic functions; related numbers; inversion formulas
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