Basic principles of adaptive differential pulse code modulation (ADPCM)

At present, the digital communication system of pulse code modulation (PCM) has been widely used in large-capacity digital microwave and optical fiber communication systems, as well as the inter-office relay transmission system of the urban telephone network. However, the existing PCM coding must adopt the 64Kbit/s A-law or μ-law logarithmic compression and expansion method to meet the quality indicators of long-distance telephone transmission voice, and its occupied frequency band is many times wider than that of the analog single-sideband communication system. In this way, for expensive long-distance and large-capacity transmission, especially for satellite communication systems, the economic efficiency of using PCM digital communication is difficult to compare with analog. Therefore, people have been committed to studying the work of compressing the frequency band occupied by digital voice, that is, trying to reduce the digital rate of digital voice under the condition of the same quality index, so as to improve the frequency band utilization of digital communication systems.
Adaptive differential coding modulation (ADPCM) is gradually developed on the basis of differential pulse code modulation (DPCM). The working principle of DPCM can be found in the relevant chapters of the principle textbook. In its implementation, it uses prediction technology to reduce the redundancy of the input signal of the quantization encoder, encodes the difference signal to improve efficiency and reduce the rate of the coded signal, which is widely used in the digitization of voice and image signals. In recent years, CCITT has determined the conversion system from 64Kb/s to 32kb/s, which converts the standard PCM code into 32kb/s ADPCM code, and then restores it to 64Kb/s PCM signal after transmission, thereby doubling the compression rate of 64Kb/s digital voice and doubling the ease of expansion of the transmission channel.
The quantizer and predictor in ADPCM are both adaptive, that is, the parameters of the quantizer and predictor can adapt to the optimal parameter state according to the statistical characteristics of the input signal. Usually, people call the speech coding method with a digital rate lower than 64Kb/s as speech compression coding technology. There are many speech compression coding methods. Adaptive differential pulse modulation (ADPCM) is a less complex method in speech compression coding. It can achieve the speech quality requirements of 64kbit/s digital rate at 32kbit/s digital rate, that is, it meets the quality requirements of long-distance calls.
When sampling a voice or video signal at a rate higher than the Nyquist rate, there is a clear correlation between the previous and next samples. When these related samples are encoded in the usual PCM system, the encoded signal will contain redundant information. If this redundant information is removed before encoding, a more efficient encoded signal can be obtained. To this end, the correlation of the signal X (nts) can be used to linearly predict future samples. The predictor is usually a tapped delay filter (i.e., FIR filter) as shown in Figure 7-12.

The predicted value of the linear predictor is:

Where ai is the prediction coefficient, which is a constant in DPCM and an adaptive variable in ADPCM. n is the prediction order. The prediction coefficient ai can be calculated based on the criterion of minimum prediction error energy. In this way, the PCM encoder quantizes and encodes the difference signal e(nTs)=x(nTs)-x∧(nTs) to achieve the purpose of ADPCM encoding.