Spectral analysis of variable-length coded digital signals

Spectral analysis is performed for a digital message produced by a variable-length encoder driven by a stationary memoryless source. In particular, closed form expressions are derived for both the continuous and the discrete part of the spectral density. The continuous part turns out to be a rational function of
z=\exp (j2\pi fT)
,where
T
is the symbol period, whereas the discrete part exhibits in general spectral lines at multiple integers of
(\lambda_{0}T)^{-1}
, where
\lambda_{0}
is the greatest common divisor of the codeword lengths. As an application of the theory explicit formulas are derived for the spectra of B
n
ZS and HDB
n
codes.