Bandlimited rational models for signal reconstruction

A rational model is proposed for reconstruction of bandlimited signals from successive observations, bandlimits, and knowledge of signal peak location. The parameters of the model may be estimated from the singular vectors of a certain double-Hankel matrix constructed from this information. In contrast to the currently popular minimum-energy approach, which has limited spectral resolution and is sensitive to noise, high spectral resolution is possible with the rational model because of its pole-zero nature. To reduce the sensitivity of the rational reconstruction to noise and modelling errors, rank reduction of the double-Hankel matrix via singular value decomposition is suggested. The singular values of the matrix provide estimates of the error in modelling the data with rational models of different orders, and so the singular value distribution can be used to select model order. This work was partially supported by SDIO/IST under contract DAAL 03-86-0111 administered by the US Army Research Office, by the Bell Communication Research’s Graduate Study Program, and by Cray Research Inc. under grants DMS9880010SC and ECS890002SC and utilized by the Cray X-MP/48 at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign.