What is nature's error criterion?
- 1 March 1954
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IRE Transactions on Circuit Theory
- Vol. 1 (1) , 76
- https://doi.org/10.1109/tct.1954.6373361
Abstract
It is well known that the Fourier series is not the only trigonometric polynomial that may be used to represent a periodic function. It is a polynomial with the property that the mean square error between a partial sum and the given function is a minimum; that is to say, it approximates the given function so as to make the mean square error a minimum. This error criterion is only one of many that could be stipulated as fixing the manner in which the polynomial approximates the given function, and from a practical standpoint it isn't even a good one for many applications because it suffers from the Gibbs phenomenon. A Tschebyscheff-like approximation or the one inherent in the Cesaro sum which converges uniformly even at points of discontinuity may be preferable in many cases.Keywords
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