Generation of a Wideband Response Using Early Time and Low Frequency Data Through the Discrete Laguerre Sequences

Abstract: The continuous orthonormal basis functions have been used to extrapolate the wideband response from early time and low frequency data. However it’s impossible to evaluate at every point of the functions. We have to sample the polynomials both in time and frequency domains before we can use them to carry out the extrapolation. The process of sampling will introduce some errors, especially for high orders and hence may destroy the orthogonality between the polynomials of various orders in a discrete sense. we introduce the discrete Laguerre functions, which are directly derived using the Z transform, and thus are exactly orthonormal in a discrete sense. The discrete Laguerre polynomials are fundamentally different from the continuous counterparts, except asymptotically when the sampling interval approaches to zero. The other advantage of using these discrete orthomormal functions is that they do not give rise to the Gibbs phenomenon unlike its continuous counterpart. Using it in the extrapolation, the range or convergence can be extended both for the scaling factor of a and for the expansion order of N, and at the same time, the quality of performance can be improved.