Spectral Shaping for Codes with P.S.D. Expressed by Rational Functions

Abstract

Based on the fact that spectral shaping of digital data signals is obtained by encoding and that there exist spectrally equivalent digital filters, the method of Justesen was applied to derive digital filters that approximate the power spectral density (p.s.d.) of a code. The (2,2,3) code, which belongs to the class of FAS (Finite Autocorrelation Sequence) codes showing a limited number of values of the autocorrelation function that are not zero, was used as an example. The spectral properties of the (2,2,3) code are thoroughly investigated in terms of autocorrelation function values and p.s.d. both as a function of normalized frequency fn and the probability of a mark p. The prediction coefficients for the digital filter implementations are derived using approximations by Markov processes of the third, fourth and fifth order. The resulting spectra are compared with those of (2,2,3) code.

Keywords

• Codes
• Digital filters
• Linear predictive coding
• Markov processes
• Spectral analysis