ON EN EDUCTION AND TXME-BANDWIDTH PRODUCTS IN SIGNAL RECONSTRUCTION *
K.S. Arun, Satya Dharanipragada · 1990
A dimensionality reduction method based on time-bandwidth products is proposed for tlie reconstruction of bandlimited, essentially time-limited signals from a small number of observations. A criterion is presented for choosing the dimension of the reduced signal space based on knowledge of the passband, time-concentration interval, energy concentration factor, and bounds on the tolerable reconstruction error. The reconstruction is constrained to lie in this lower dimensional signal space, and parameters characterizing the reconstruction are obtained from the d ata by solving a linear system of equations. For certain sampling patterns the system is ikonditioned, and a gecond rank reduction is needed to reduce the deleterious effects of observation noise and modeling error. A novel criterion for rank selection based on knowledge of bounds on noise power and modeling error is presented.