Logarithmic PCM Encoding Without Diode Compandor

Instantaneous companding is a useful technique for the improvement of the transmission quality of PCM systems. In this paper various nonlinear encoding and decoding techniques without using diode compandors are stated with a focus on the logarithmic decoders, which are composed of cascaded attenuators. Hyperbolic sinusoidal law is also derived from the logarithmic law and is obtained by an attenuation line decoder. These nonlinear laws are attained on the attenuation-linear basis. Likewise, various passive decoders on the immittance-linear basis can be considered. In this case the nonlinear law is expressed by a rational function of the digital variable
x
. Also a decoder based on the multinomial expansion is introduced, whose nonlinear law is given by a polynomial of
x
. It is shown that the hyperbolic sine curve provides more uniform signal-to-noise characteristics for some range of the mean speech volume, while the modified hyperbolic law yields as high signal-to-noise ratio as is obtained by the exponential law without great loss in the signal-to-noise ratio for louder speech. A few experimental studies of these decoders are described.