Formulation of The Interpolation Problem
A trigonometric polynomial of degree n has the form
This expression contains 2n + 1 coefficients, a0, a1, … an, b1, …, bn, and we wish to compute those coefficients so that the function passes through N points:
Since the trigonometric polynomial is periodic with period 2π, it makes sense to assume that
(Note that we do not in general require these points to be equally spaced.) The interpolation problem is now to find coefficients such that the trigonometric polynomial p satisfies the interpolation conditions.
Read more about this topic: Trigonometric Interpolation
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