Digital Representation of Signals

Abstract

As it was discussed in Sect. 2.1, signal digitization can be treated in general terms as determination, for each particular signal, of an index of the equivalency cell to which the signal belongs in the signal space and signal reconstruction can be treated as generating a representative signal of the cell from its index. This is, for instance, what we do when we describe everything in our life with words in speaking or writing. In this case this is our brain that makes the job of subdividing “signal space” into the “equivalency cells” of notions and recognizing which word (cell index) corresponds to what we want to describe. The volume of our vocabulary is about 10 ⁵ ÷ 10 ⁶ words. The variety of signals we have to deal with in signal processing and especially in optics and holography is immeasurably larger. One can see this from a simple example of the number of different images of, for instance, 500 × 500 pixels with 256 gray levels. This number is 256 ^500×500. No technical device will ever be capable of storing so many images for comparing them with input images to be digitized.