 added to the neighboring pixels that have not been quantized yet. This is sometimes referred to as error diffusion as well. Figure 1.11 illustrates the level of quality improvement that can be achieved by spatially spreading the quantization noise over the image pixels. Notice that the root mean square (r.m.s.) of the quantization error is almost the same for the threshold- ing and dithering algorithm. However, in audio engineering, dithering can be used to spread the quantization noise over the frequency range to minimize the perceptual distortion. Surprisingly, this is done Chapter 1 Voice Transmission Frequency (Hz) Frequency (Hz) Frequency (Hz) Fig. 1.12 Impact of dithering: (a) spectrum of the original sine wave, (b) spectrum of the quantized sine wave without dithering, (c) spectrum of the quantized sine wave with dithering. by adding low-level random noise to the signal. In fact, the nonlinear effect of the quantiza- tion leads to audible distortion. This is mainly because of the "stairsteps" waveform of the quantized signal and is more significant for signals of sufficiently low level to be comparable with the quantization step size. The idea is to add random noise to the waveform to "break up" the statistical determinability of the stairstepped waves. In fact, by adding dither to the audio signal with a level that is approximately half the level of the least significant bit (LSB), the frequency selective noise (distortion) is eliminated at the cost of a very-low-level con- stant noise. Because the human brain is less sensitive to a constant background noise, the perceptual quality will be improved. As an example, consider a sine wave at the frequency of 100 Hz that is quantized using 16 quantization levels. Figure 1.12(a) shows the spectrum of the sine wave before quantiza- tion. As expected, the power spectrum contains a single peak at 100 Hz. Figure 1.12(b) shows the power spectrum of the quantized signal without dithering. As can be seen, the signal contains many harmonic distortion components. Figur