Codes with a multiple spectral null at zero frequency

Codes whose spectral density and its lower order derivatives vanish at zero frequency are investigated, and necessary and sufficient conditions for the spectral properties are given. In particular, for the most common balanced alphabets, a complete characterization is furnished for the class of symbol-by-symbol codes with vanishing spectrum and second derivative. The fundamental results are extended to block codes, and suitable criteria for their design are given. Specific examples of binary and ternary block codes are presented; their performance in terms of low power content at low frequencies compares advantageously with that of some conventional codes.>