Compression of Transmission Bandwidth Requirements for a Certain Class of Band-Limited Functions

A study of source-encoding techniques that afford a reduction of data-transmission rates is made with particular emphasis on the compression of transmission bandwidth requirements of band-limited functions. The feasibility of bandwidth compression through analog signal rooting is investigated. It is found that the th roots of elements of a certain class of entire functions of exponential type possess contour integrals resembling Fourier transforms, the Cauchy principal values of which are compactly supported on an interval one th the size of that of the original function. Exploring this theoretical result it is found that synthetic roots can be generated, which closely approximate the th roots of a certain class of band-limited signals and possess spectra that are essentially confined to a bandwidth one th that of the signal subjected to the rooting operation. A source-encoding algorithm based on this principle is developed that allows the compression of data-transmission requirements for a certain class of band-limited signals. The utility of this algorithm is illustrated by a digital computer simulation of a facsimile telegraphy system. The scanning and recovery of several alphanumeric character images is simulated. Recognizable replicas of the original pattern are retrieved after 6-to-1 bandwidth compression.