Redundant Alphabets with Desirable Frequency Spectrum Properties

When alphabets of digital symbols are used to represent information for data processing, storage, and transmission, redundancy in the alphabets is traditionally used for the purpose of error compensation. This paper deals with alphabets of redundant codes, both binary and higher level, where the emphasis is on using redundancy to produce code alphabets with unique properties in their frequency spectra that can be exploited in the design of the system in which they are used. In particular, techniques are presented for synthesizing alphabets that produce spectral nulls at frequencies 1/kT, where T is the duration of a word element. Some of the interesting alphabets are a 10-word, 5-bit alphabet with spectrum zero at 1/2T; a 10-word, 6-bit alphabet with spectrum zero at 1/3T; a 36-word, 8-bit alphabet with zero at 1/4T; and a 36-word, 8-bit alphabet with zeros at both 0 and 1/2T.