Differential Pulse Code Modulation
The Differential Pulse Code Modulation ( DPCM ) is a pulse modulation method , which is a time-discrete signal into a time and value-discrete digital signal are reacted. It is an extension of pulse code modulation (PCM) and is a preliminary stage to adaptive differential pulse code modulation (ADPCM). In DPCM, differential values of successive sampled values are formed, which leads to a data reduction in signal sequences with high autocorrelation , such as digital audio signals , for example . DPCM was developed by C. Chapin Cutler at Bell Laboratories in 1950 .
functionality
A DPCM system consists of an encoder (modulator) and a decoder (demodulator) with a channel in between . From the sequence of the data source to be transmitted , denoted by x [n] in the figure opposite , the difference sequence e [n] is first formed:
![{\ displaystyle e [n] = x [n] -x_ {D} [n-1] \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6845ddf342bd2fdc415f856fd799f0957da0c08e)
is fed to the quantizer Q , which uses it to form the digital signal . This is transmitted to the decoder via the channel as well as fed to an addition stage, which
![{\ displaystyle e [n]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9333d516ef86093cecb2ccbbc8097e5136758c0d)
![{\ displaystyle e_ {Q} [n]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a83a2f88dd25f345110609737cc13fa27283d6b4)
![{\ displaystyle x_ {D} [n] = e_ {Q} [n] + x_ {D} [n-1] \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30e94de499997e4fe3e537ffece29dd6e7e96b3d)
forms. The value is stored for the duration of one sampling period, shown in the figure as z −1 . The output of the storage element ( English tap ) is fed to the input stage for difference formation.
As an alternative, there is also another DPCM process, which shows the difference between two input values directly at the input
![{\ displaystyle e '[n] = x [n] -x [n-1] \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/314a9b32335c0dd1d387eba73b2ee9fe37621bcd)
forms. This form of DPCM has the disadvantage of not compensating for quantization noise and only plays a subordinate role in practical applications.
To reconstruct the received sequence, the decoder uses a tap and an addition stage to create the original signal sequence using the following relationship:
![{\ displaystyle e_ {q} [n]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bc6de4be33b0166b904b3c57a47d02bcaece6d25)
![{\ displaystyle x_ {D} [n]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f763553c1bc2ca65f292afe03bcf438f5f86bfc)
This form of DPCM with only one storage element for the encoder or decoder represents the original and simplest DPCM system. As an extension with predictive coding , a sequence of p samples can be used to form the difference. The difference signal is then formed by
![{\ displaystyle e_ {p} [n]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4d76e3412be18ea450e4a695b392250e1e8a206)
![{\ displaystyle e_ {p} [n] = x [n] - \ sum _ {i = 1} ^ {p} a_ {i} \ cdot x_ {D} [ni] \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb39d4062412d208c37d6cb58a660836551a7dd)
with the prediction coefficients which represent weighting factors. Depending on how these prediction coefficients are selected in relation to the course of the input signal sequence , the scope of the difference signal can be reduced with constant information content.
![x [n]](https://wikimedia.org/api/rest_v1/media/math/render/svg/864cbbefbdcb55af4d9390911de1bf70167c4a3d)
Individual evidence
- ↑ Patent US2605361 : Differential Quantization of Communication Signals. Filed June 29, 1950 , published July 29, 1952 , inventor: C. Chapin Cutler.
literature
- John G. Proakis, Masoud Salehi: Communication Systems Engineering . 2nd Edition. Prentice Hall, Upper Saddle River NJ 2002, ISBN 0-13-095007-6 .