An Improved Estimate of the Accuracy of Trigonometric Interpolation

Utilizing the concept of aliasing, we are able to obtain a new estimate of the accuracy of trigonometric interpolation. For functions with K continuous derivatives, we show that the n-point sum gives approximation to order $O(n^{ - (k - 1)} )$. When $K = 2$, this improves the usual accuracy estimate of $O(n^{{{ - 1} / 2})} )$.