The Spectral Density of a Coded Digital Signal

In recent years, increased interest has been focused on more complex multi-alphabet, multi-level codes. 1-4 Such codes are designed to produce a digital pulse train with specific spectral properties making it suitable for transmission over digital repeatered lines. These properties generally include the absence of a dc component and a strong spectral component from which timing can be extracted. This paper presents a method for calculating the spectral composition of the pulse trains resulting from the use of these codes. The procedure is applicable to a wide variety of codes. A code may be defined as a set of mappings from a set of input symbols (or words) to a set of codewords. Each mapping is called an alphabet. The code may use different alphabets depending upon the state of the coded signal. 1 It is desirable for unique decipherability that the set of mappings be one-to-one, i.e., that no matter to how many alphabets a codeword belongs, it always corresponds to the same input symbol. However, this restriction will not be imposed here. In general, when the code is applied to a sequence of input symbols, the resulting encoded signal is a stochastic process, the statistics of which depend on the input symbol sequence statistics and the code statistics. For convenience, a random input symbol sequence will be assumed so that the input symbols are equally likely. Even if the 921