The Linear Interpolation Method: a Sampling Theorem Approach

A lecture note introducing the sampling theorem as an interpolation method is presented. The relationship between piecewise linear approximation and the sampling theorem is highlighted by the use of triangular pulses instead of sampling functions. Furthermore, a comparison of the linear interpolation with a series on a nonorthogonal basis composed of equally spaced triangular pulses is provided. The interpolation uses the sample values of Artigo submetido em 24/05/2001 1a. Revisão em 8/10/2002; 2a. Revisão 21/10/2002 Aceito sob recomendação do Ed. Assoc. Prof. José R. C. Piqueira the function whereas the series coefficients are obtained by minimizing the quadratic error between the original function and the series.