The standard for the digital representation of voice signals in telephone networks is given by the pulse code modulation (PCM) format. In PCM the voice signal is filtered to obtain a lowpass signal that is limited to W = 4 kHz. The resulting signal is sampled at the Nyquist rate of 2 W = 8 kHz. Each sample is then applied to an m = 8 bit quantizer. The number of levels in the quantizer is therefore 256. The type of quantizers used in telephone systems are nonuniform quantizers. A technique called companding is used so that the size of the intervals increases with the magnitude of the signal x. The SNR formula is given by

Because m = 8, we see that the SNR is 38 dB. Note that an SNR of 1 percent corresponds to 40 dB. In the backbone of modern digital telephone systems, voice signals are carried using the log-PCM format, which uses a logarithmic scale to determine the quantization intervals. The ISDN standard extends the use of the PCM format all the way to the telephone at the user's end.

the Digital Audio Compression (AC-3) that is part of the U.S. ATSC highdefinition television standard involves five channels (left, right, center, left-surround, right-surround) plus a low-frequency enhancement channel for the 3 Hz to 100 Hz band.

The derivation for the performance of the uniform quantizers assumes that we know the exact dynamic range — V to V in which the signal values will fall. Frequently the system does not have sufficient control over signal levels to ensure that this is the case. For example, the distance a user holds a microphone from his or her mouth will affect the signal level. Thus if a mismatch occurs between the signal level for which the system has been designed and the actual signal level, then the performance of the quantizer will be affected. Suppose, for example, that the quantizer is designed for the dynamic range —V to V and the actual signal level is in the range — V/2 to V/2. Then in effect we are using only half the signal levels, and it is easy to show that the SNR will be 6 dB less than if the signal occupied the full dynamic range. Conversely, if the actual signal level exceeds the dynamic range of the quantizer, then the larger-magnitude samples will all be mapped into the extreme approximation values of the quantizer. This type of distortion is called clipping and in the cassette recording systems that you are surely familiar with is indicated by a red light in the signal-level meter.

Figure 12.20 shows the speech waveform for the following sentence: The speech signal level varies with time. The waveform is about 3 seconds long and was sampled at a rate of 44 kHz, so it consists of approximately 130,000 samples. Large variations in signal levels can be observed.

One way of dealing with variations in signal level is to actually measure the signal levels for a given time interval and to multiply the signal values by a constant that maps the values into the range for which the quantizer has been designed. The constant is then transmitted along with the quantizer values. These types of quantizers are called adaptive quantizers. A passive way of dealing with variations in the signal level is to use nonuniform quantizers where the quantizer intervals are roughly proportional to the signal level. The companders used for telephone speech are an example of this.

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