SYSTEM AND METHOD FOR COMMUNICATING DIGITAL INFORMATION USING TIME-AND-FREQUENCY-BOUNDED BASE FUNCTIONS

Systems and methods for efficiently conveying one or more communication channels over a transmission medium. Communication is effected by transforming an incoming digital bit stream into a Hermite-Gaussian information stream that includes a plurality of Hermite-Gaussian packets. This transformation is accomplished through the use of a plurality of Hermite-Gaussian basis functions. The Hermite-Gaussian information stream is then transmitted over the transmission medium. More particularly, digital bit streams carried on one or more incoming channels may be in the form of binary "on" and "off" bits. These digital bits are converted into a plurality of Hermite-Gaussian waveform components which together comprise a Hermite-Gaussian packet. The conversion process maps each of respective incoming digital bits to a corresponding one of a group of Hermite-Gaussian functions. Optionally, this mapping process could be implemented sequentially, or in parallel form, such that a first bit is mapped to a first Hermite-Gaussian function, a second bit is mapped to a second Hermite-Gaussian function, and so on, until the Nth Hermite-Gaussian function is reached, whereupon the process cycles back to the first Hermite-Gaussian function. In any case, the presence of a "1", "on", or "high" bit enables the corresponding Hermite-Gaussian function, whereas the presence of a "0", "off", or "low" bit disables the corresponding Hermite-Gaussian function. When enabled, each respective Hermite-Gaussian function specifies the transmission of a corresponding Hermite-Gaussian waveform component. Each waveform component is substantially confined within a range of values in both the frequency and time domains.