Baseband line codes via spectral factorization

A description is given of a methodology for designing baseband line codes with prescribed spectral nulls in the transmitted spectrum. These codes have the property that the transmitted power is adjustable (with a concomitant change in spectral shape, i.e. null width) and can be made arbitrarily close to the innovations power, while keeping the minimum distance between signal points (or sequences) constant. The essential design step requires the spectral factorization of a certain trigonometric polynomial. The line code that results can easily be used in conjunction with a large class of trellis-coded modulation schemes. Specific baseband codes are constructed using a representation of the general theory that involves a dither variable, which is used to create integer symbols and to minimize the size of the symbol alphabet. Emphasis is on the design of line codes with a double null at DC using the symbol alphabet {±1, ±3}