Construction of Codewords and Pulse Shapes to Meet Spectral Requirements

Line codes (in transmission systems) and recording codes (in magnetic and optical recording systems) are constrained sequence codes used to control the frequency-domain and time-domain characteristics of encoded signals. Pulse shaping is also used to achieve the required signal characteristics in a wide variety of communication systems. In this paper a new technique is outlined for the construction of codewords and pulse shapes to meet specified spectral constraints. The signal is interpreted as a block-coded sequence of overlapping or non-overlapping waveforms weighted by symbol values, and a general expression is given for the power spectral density of this signal. Based on this expression, the values of the symbols are evaluated in order to satisfy the most significant terms of a Fourier series representation of the desired spectral response. Examples and simulation results presented in this paper confirm the validity of this approach.