Orthogonalizing the equally spaced impulse responses of nonideal low-pass filters

Orthogonal bases allow a simple and decoupled computation of the generalized Fourier coefficients in a signal reconstruction context. On the other hand, nonuniform orthogonal bases require a large number of stored functions in the receptor. This paper presents a procedure to orthogonalize a set of linearly independent and uniform functions. The main characteristic of the algorithm is to maintain the uniformity, preserving both simplicity and orthogonality. Then, this algorithm is devoted to analyze the set of equally spaced impulse responses of realizable low-pass filters. Two examples are presented, attesting the better signal reconstruction obtained by generalized Fourier series in contrast with the direct sampling theorem results