Question 9.1: Let us assume that we are sampling a 4-kHz voice signal with...

The Nyquist rate is 8 kHz; thus, the oversampling ratio is 1,000. This will result in 0.5 log_{2} (1,000) = 5 bits extra resolution. Since we started with 8 bits, the OSR of 1,000 provides a total of 13-bit accuracy.

Is quantization really like noise? Consecutive 8-MHz samples of a voice signal would be highly correlated; as a result, there could also be correlation in the quantization error. Consequently, quantization power would not be reduced by averaging. For samples where noise is correlated from sample to sample, one can use dithering (adding a small random signal) in \Sigma \Delta modulation to randomize the correlated quantization noise power. Integral (large-scale) nonlinearity is also not improved by oversampling. In frequency synthesis, any correlation between noise samples in the time domain generates spurious tones (spurs) in the frequency domain. In contrast to white noise, the spurs are located at particular frequencies that cannot be reduced by averaging when the oversampling ratio increases. Thus, the oversampling technique has no impact on fractional spurious tones, although it can reduce random white noise. In frequency synthesis, randomization techniques are needed to break the correlation and repeated patterns and, thus, to spread the spur energy over the frequency band. The randomization process results in a quasiwhite noise characteristic that can then be reduced by oversampling techniques. In conclusion, oversampling trades speed for resolution and allows the use of high-speed digital circuits instead of precise analog circuits, resulting in design simplicity and a certain amount of design freedom.