e 1.12(c) shows the spectrum of the quantized signal when dither noise was added to the signal before quantization. It can be seen that, with dithering, the harmonic distortions are eliminated at the cost of overall shift in the noise floor. The dither noise can be selected from a Rectangular Probability Density Function (RPDF), a Triangular Probability Density Function (TRDF), or a Gaussian PDF. RPDF dither- ing is the most basic method where a uniformly distributed noise is generated and added to the signal before it is quantized. The dither noise can be also reduced by employing an error feedback loop around the quantizer, which operates as a noise-shaping filter. Peak clipping is another source of distortion in the quantization process. Peak clipping will take place if the signal amplitude is larger than maximum quantization level. In practice, signal limiters are used to avoid peak clipping. A uniform quantizer is optimum when the input has uniform distribution. However, this might not be the case for speech signals with a high crest factor. In fact, the quantization process can be optimized (i.e., minimum quantization error) by considering the PDF of the input signal. Experimental results have shown that the probability distribution of a voice signal, Px(x), can be approximated by a Laplace distribution in the form (Carlson, Rutledge, and Crilly, 1968) (1.17) Pulse Code Modulation Laplace Experimental Distribution Results Model Time (s) Voice Sample Amplitude Fig. 1.13 (a) Six-second sample of a voice segment; (b) PDF for the voice signal in Figure 1.10(a). As shown by Figure 1.13(b), this approximation is very accurate, especially when the number of samples is high (long-term approximation). The experimental results presented in Figure 1.13(b) belong to six seconds of a voice segment (Figure 1.13(a)). As is evident, the frequency of samples with smaller amplitudes is considerably high compared to high- amplitude samples. In other words, efficient speech quantizations require nonuniform quan- tization level