Peak Signal-to-Noise Formulas for Multistage Delta Modulation with RC-Shaped Gaussian Input Signals

Delta modulation (DM) has been extensively studied,1_H and following its integration onto a chip,9 it is being increasingly used in industrial applications. The salient advantages of DM are robustness to transmission errors; tolerance to clock jitter; simple filtering requirements; suitability for encryption; and low complexity resulting in inexpensive implementation. In typical applications, the ratio fp/fc is 10, where fp is the transmitted bit rate and fc is the bandwidth of the message signal. However, DM does not efficiently improve its s/n with increasing f p / f c particularly when compared to pulse code modulation ( P C M ) . A S a consequence, DM is rarely used to encode high-quality audio signals because of the excessive fp/fc ratios required. In DM, the quantization noise is dependent on the error e{t) between the input signal x{t) and a locally reconstructed version y(t) (formed by locally decoding the transmitted bit stream). Thejy(i) signal essentially tracks x(£), and the polarity of the transmitted bit is identical to 347