Distortionless data transmission with minimum peak voltage

Abstract

Knowing that the tails of the ideal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sin \pi t/ \pi t</tex> pulse represent a divergent series, the problem is stated of finding distortionless bandlimited waves which give rise to a minimum of the worst peaks of voltage that can appear on the channel in unit-height binary transmission. The optimization problem is then solved for all sampling rates up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</tex> the Nyquist rate by the unique wave which never gives rise to more than one volt on the channel, just the magnitude of the data bits themselves. An upper bound is established on the worst channel voltage at higher rates by means of a class of pulses whose spectrum reduces to the optimum when the sampling rate parameter is chosen to be <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</tex> the Nyquist rate. A time-domain optimization principle is stated which deals with zero manipulation, and the implications for the concept of dimensionality are discussed. The principal results of this paper are related to other system concepts, including timing-jitter immunity and duobinary transmission.