From Analog Signals to Digital Information

Many information-processing applications are based on digital data although the origin of most sources of information is analog. A new signal sampling and representation framework for such purposes is introduced in this work. We use prolate spheroidal wave functions (PSWF) to represent analog signals by digital information. The proposed method can be applied to reconstruct signals on a finite interval from a finite number of discrete samples. It is shown that, contrary to the Nyquist approximation, the reconstruction error of the proposed technique can be made as small as desired. The new method is applicable to general signals including twodimensional sources of images. Experimental results are presented and discussed. Our conclusion is that the proposed approach to signal representation using PSWF could be superior to presently available methods and may be instrumental in most practical cases of digital signals, which are naturally of finite support.