Synthesis of Band-Limited Orthogonal Signals for Multichannel Data Transmission

In data transmission, it is common practice to operate a number of AM data channels through a single band-limited transmission medium. The system designer is faced with the problem of maximizing the overall data rate, and minimizing interchannel and intersymbol interferences. In certain applications, the channels may operate on equally spaced center frequencies and transmit at the same data rate, and the signaling intervals of different channels can be synchronized. For these applications, orthogonal multiplexing techniques can be considered. Several 1775 178(3 T H E B E L L SYSTEM TECHNICAL JOURNAL, D E C E M B E R I960 orthogonal-multiplexed systems developed1,2 in the past use special sets of time-limited orthogonal signals. These signals have widely spread frequency spectra (e.g., a sin x/x spectrum). Consequently, when these signals are transmitted through a band-limited transmission medium at a data rate equivalent to that proposed in this paper, certain portions of the signal spectrum will be cut off and interferences will take place. For instance, the interferences because of band-limitation have been computed3 for a system using time-limited orthogonal sine and cosine functions. This paper shows that by using a new class of band-limited orthogonal signals, the AM channels can transmit through a linear band-limited transmission medium at a maximum possible data rate without interchannel and intersymbol interferences. A general method is given for synthesizing an infinite number of classes of band-limited orthogonal time functions in a limited frequency band.