Trigonometric Interpolation Based on Summation of Fourier Series F_{i}^{\delta} with Data-Related Delta-Function Property F_{i}^{\delta}\left(x_{j}\right)=y_{j}\delta_{ij} (Analogy to Lagrange Form of Interpolation Polynomial)

Full analogy to the Lagrange form of the interpolation polynomial is constructed for Fourier series. As a straightforward consequence one gets the ability to extend an existing trigonometric interpolation to additional data point(s).