RECONSTRUCTION OF FUNCTION USING CARDINAL SERIES - YAHYA (NIM : 20114005), ARNASLI
Sampling Shannon theorem states that in a special case a function can be reconstructed through its values at sample points. The series formed in the sampling Shannon theorem is defined by cardinal series. The cardinal series is a generalized Fourier series which uses the family of sinc functions that form an ortogonal basis for the space of L2 functions whose Fourier transforms vanish outside some compact set. Band limited is one of condition for the functions to be reconstructed. In the application, this condition is not always easy to be obtained. In such a case, what we ca do is assume that the function is band limited on some interval. This can cause an aliasing error. Another problem is the cardinal series contains infinity many samples, which is impossible to reach. This will cause a truncation error. Furthermore, we will study aliasing error and truncation error of cardinal series and their upper bounds.