Generalized Spectrum of Interpolants: Part II - Design and Applications

Continuing discussion in A. Bhandaru and N.V. Kalpakan (2007), in this paper we examine we propose a better technique for reconstruction of continuous time signals. The basis functions used for reconstruction in this paper are based on design examples extending the formulations presented in A. Bhandaru and N.V. Kalpakan (2007), An expression for calculation of the oversampling factor is derived, which is an important parameter for designing filters which occupy excess bandwidth (a realistic situation, ideal filters don´t exist). This technique proves to be a superior solution in terms of the L₂ error, when compared with existing and classical solutions like the Nyquist Shannon Interpolation method (especially when using truncated interpolants). Using the spectral properties presented in A. Bhandaru and N.V. Kalpakan (2007), one can show that linear combination of an interpolant is a new interpolant. We explore into possibilities of design of reconstruction filters which have a better decay than the conventional sinc.