Upper bound for signal/noise ratio for instantaneously companded delta-modulation systems

Instantaneously companded delta modulators are able to produce a wide range of step changes in the feedback waveform, and the step change can vary by substantial amounts between adjacent clock periods. In spite of this ability, the peak s.n.r.s achieved by these modulation systems are not substantially greater than those of the linear delta-modulation ones. To assess the potential of instantaneously companded delta-modulation systems, an optimum one is considered, and its s.n.r. as a function of clock rate is compared with those of the linear and 2nd-order constant-factor delta-modulation codecs. It is shown that the optimum codec has much the larger s.n.r., but exchanges this s.n.r. for increasing channel bit rate in a way similar to that of the linear delta-modulation system.