Abstract
In most cases evaluation of Fourier series requires that special summation methods be applied or that the coefficients of the series be suitably modified to suppress strong oscillations at discontinuties of the approximated function. All these methods may be described as a substitution of the Dirichlet kernel by other kernels. In this paper eight of these kernels are briefly reviewed and compared with a ninth kernel which is based on Chebyshev polynominals. A closed-form representation has been derived for the Fourier coefficients of this kernel as well as a recursive relation for their practical computation. Furthermore, an error criterion is given which allows the determination of an upper bound of the difference between Fourier series and approximated function provided upper limits on both the variation and the second derivative of the latter are known.
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