Digital signal interpolation using matrix techniques and the Whittaker cardinal function

The infinite Whittaker summation and Shannon's sampling theorem both use the weighted sum of sinc functions (the 'Cardinal' function) in the interpolation algorithm. When the number of original samples is approximately equal to twice the product of duration (T) and bandwidth (W), and when it is desired to increase the number of samples by powers of 2, the interpolation process can be written as a matrix equation. It is shown that when the original sample set is periodic, the matrix elements converge to simple cosecant and cotangent functions. An extensive computer program which implements the algorithms is described. Numerous signals are processed and the results presented in plots and tabular form. The work is ended with an entire chapter suggesting areas for follow-on work.