antizing Noise Quantizing causes signal distortion because the sample values no longer rep- resent accurate values of the analog signal. Usually this distortion caused by rounding off in quantizing is small compared to the signal value. The maxi- mum distortion, that is, maximum quantizing error, is half of the distance between quantum levels. This distortion is heard and theoretically modeled as noise; see the quantizing error curve in Figure 3.9. We can imagine that the decoder first receives accurate sample values and produces a perfect origi- nal signal. Then quantizing error is added on top of the perfect signal just as we hear, for example, background noise on top of an ideal voice or music signal. The rounding off causes an error that is independent of the message because quantizing levels are close to each other and we can assume that the signal has the same probability to be anywhere between two levels at a certain sampling instant as shown in Figure 3.10. This error can be assumed to have a uniform probability density function and a zero mean. When we define the Introduction to Telecommunications Network Engineering Analog Quantizing signal Maximum signal to levels quantizing noise ratio: S/N <= 4.8 + 6.0 n dB Quantizing where n is the number distortion bits/binary sample word or noise Practical figures are much (10-30 dB) lower. Sampling instants The more levels (the more bits/sample, the higher bit rate) we use, the better performance we get (i.e., higher signal to noise ratio). Figure 3.10 Quantizing noise and SQR. signal to have values between -1 - ... +1, it can be shown quantum noise power is equal to the variance of quantizing error and is given by (3.5) where N = 02 = = quantization noise power and q = the number of quantum levels. [Equation (3.5) gives the variance O a of uniform distribution with a value of q/2 from -1/9 to 1/q. The variance corresponds to the noise power N when the mean is zero.] We see that if the number of quantum levels is increased, quantizing noise power decreases rapidl