A discrete trigonometric interpolation method

Abstract

Interpolation theory is a necessary and crucial tool for many applied engineering sciences.In this paper, we propose a new kind of 2-period interpolation of functions with period 2π at the nodes x _k = x _k,n = kπ/n, (k = 0,1,…, 2n − 1).We find out the necessary and sufficient conditions for regularity of this new interpolation problem.Moreover, a closed form expression for the interpolation polynomial is given.Our interpolation is of more practical significance.Our results provide the theoretical basis for using our interpolation in practical problems.

Keywords:

• Interpolation
• Trigonometric polynomial
• Existence and uniqueness
• Signal and image processing
• Computer vision

C.R.Categories:

• G.1.2
• I.4.4
• I.5.3

^*This work was supported by the Natural Science Foundation of China, Grant No.69705002, and State Commission of Science and Technology of China, Grant No.G1998030503.

^† [email protected]

^*This work was supported by the Natural Science Foundation of China, Grant No.69705002, and State Commission of Science and Technology of China, Grant No.G1998030503.

^† [email protected]

Notes

^*This work was supported by the Natural Science Foundation of China, Grant No.69705002, and State Commission of Science and Technology of China, Grant No.G1998030503.

^† [email protected]