* Assumes signal amplitudes and quantization errors are uniformly distributed.

* Assumes signal amplitudes and quantization errors are uniformly distributed.

The effect of quantization noise may be reduced by varying the size of the quantization steps, without adding to their number, so as to provide smaller steps for weaker signals. For a given number of quantization levels, coarser quantization is applied near the peak of large signals, where the larger absolute errors are tolerable because they are small compared to the larger signal amplitudes. These techniques are commonly applied to voice transmission, where the speech waveform is compressed at the transmitter end prior to digitization, and expanded at the receiver. Taken together, the compressor and expander are called a compandor.

The number of bits per sample is determined by the mission requirements. The Jet Propulsion Laboratory typically uses 256 shades of gray (i.e., n = 8) in differentiating voltages from its imaging sensors, and 32 (n = 5) is normally used for low-definition, black-and-white TV transmission. The length of the digital word selected depends on the precision one requires for the application. For example, we do not need this precision for satellite equipment temperatures, whereas scientific measurement may require a highly precise data link, if justified by the sensor accuracy.

The data rate is the number of samples per second times the bits per sample, or the number of bits per second, abbreviated bps. Thus a digitized voice circuit in a commercial telephone network requires 8 ksamples/s times 8 bits/sample for a data rate of 64 kbps. Table 13-5 lists other examples.

The cellular-satellite systems are using methods for modulation, demodulation, and forward error correction that greatly reduce the data rates needed for transmission. For example, the Globalstar system uses code division multiple access with Reed-Solomon coding for forward error correction and Viterbi decoding. It sends voice through a variable-rate encoder/decoder at an average rate of 9.6 kb/s, and can reduce to a 4.8,2.4 or 1.2 kb/s rate under stress. These rates are much less than those discussed above, and in Table 13-5, and represent new methods of coding digital data. With these

* In dB, the signal-to-quantization noise ratio is 6n. See Sec. 13.3 for the definition of dB.

TABLE 13-5. Bit Rate Required to Transmit Analog Information Over a Digital Communication Link. The bit rate of digitized, or pulse code modulated (PCM), voice can be reduced by transmitting only the changes in amplitude between consecutive samples. This technique is known as Delta PCM.

Fretl-. fm (Hz)

Sampling Frequency (Samples/s)

Number Bits Per Sample n

Data Rate R (bps)

Voice (PCM)



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