Synthesis of spectral shaping block codes for PAM

A formula for the continuous part of the power spectral density of a block coded digital PAM signal is well known for the case of independent blocks. Based on this formula, a procedure is proposed for the synthesis of block codes yielding a polynomial approximation to a desired signal power spectral density. The code is defined by a matrix multiplication over the set of real numbers. An expression is also found for the length of the codewords and source words in terms of the degree of the approximating polynomial and the cardinality of a particular subset of its real zeros.