By Topic

What is nature's error criterion?

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Guillemin, Ernst A. ; Dept. of Electrical Engineering Massachusetts Institute of Technology Cambridge 39, Massachusetts

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.

Published in:

Circuit Theory, IRE Transactions on  (Volume:1 ,  Issue: 1 )