Theory of syllabic compandors

The paper deals with the theory of compressors and expanders in which the gain is adjusted automatically at syllabic rate and follows the envelope of the signal. It is shown that, provided that the compressor and expander are ideally complementary, there will be no overall waveform distortion in the expander output if the circuit connecting them is distortionless over the frequency band occupied by the line signal. Fundamentally this must be wider than that of the uncompressed input signal, but with telephone compandors having the parameter values normally adopted, the effect of this inflation of the frequency band is negligible. Expressions are derived for the transient response and distortion products of the line signal, and the effect of departures from the above ideal conditions on the overall distortion is investigated. Complex compressors and expanders incorporating more than one variable-loss device are also analysed, and it is shown that, within a certain class, all cases can be reduced to an equivalent simple compressor and expander. Special characteristics are obtained with more elaborate compandors not falling in this class, and some examples and possible applications are discussed.