Spectral density distributions of signals for binary data transmission

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Abstract
The analysis of spectral density distributions of transmissions is of particular interest in the assessment and comparison of high speed digital data transmission systems. Where information rates are of the order of magnitude of the bandwidth available, the particular waveforms used become significant with regard to the bandwidth utilization of the link. On the assumption that all messages are equally likely, it would appear reasonable to use the average spectral density distribution of a random message as one basis for formulating the bandwidth requirement of a particular transmission system.In this paper, a general method of determining the average spectral density distribution directly in the frequency domain is developed. The emphasis is, however, on types of waveform which are of interest in high speed transmission, and various particular cases are discussed in detail. It can be argued in the case of f.m. that to avoid discontinuities in the waveform, the signal can be generated by switching between locked oscillators, and for a smooth transition—a condition for minimum high frequency components—a digit of the higher frequency must contain an integral number of cycles more than a digit of the lower frequency. Waveforms with these restrictions are discussed for a wide variety of frequencies. The distributions for relevant p.m. systems are derived also. The spectral density distribution for f.m. at 600 bauds with frequencies of 1200 c/s and 1900 c/s (of interest with regard to G.P.O. transmissions) are also determined and results presented. Finally, the analysis of a partrandom message is presented as an example of this type of problem.

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