DPCM - Differential Pulse Code Modulation Diese Site wurde kopiert von http://www.rasip.fer.hr/research/compress/algorithms/fund/pcm/dpcm/index.html
Differential pulse code modulation (DPCM) is a
procedure of converting an analog into a digital signal in which an analog
signal is sampled and then the difference between the actual sample value and
its predicted value (predicted value is based on previous sample or samples) is
quantized and then encoded forming a digital value. DPCM code words represent differences between samples unlike PCM where code
words represented a sample value. Basic concept of DPCM - coding a difference, is based on the fact that most
source signals show significant correlation between successive samples so
encoding uses redundancy in sample values which implies lower bit rate. Realization of basic concept (described above) is based on a technique in
which we have to predict current sample value based upon previous samples (or
sample) and we have to encode the difference between actual value of sample and
predicted value (the difference between samples can be interpreted as prediction
error). DPCM compression depends on the prediction technique, well-conducted
prediction techniques lead to good compression rates, in other cases DPCM could
mean expansion comparing to regular PCM encoding. http://www.rasip.fer.hr/research/compress/algorithms/fund/pcm/dpcm/DPCM_files/image012.gif
is current sample and
is predicted value, predicted value is formed using prediction factors and
previous samples, usually linear prediction is used, so predicted value can be
given as a weighed linear combination of p previous samples
using , weighting
factors: Difference signal is then: DPCM conducted on signals with correlation between successive samples leads
to good compression ratios. If we apply facts mentioned in DPCM description and Fig 1. and Fig 2. on
image compression
is the current pixel value and
is formed using p pixels prior to current pixel.
is differential image formed as difference beteween actual pixel and previos
pixels (as described above for any signal). It is important to point out that in forming a prediction reciever i.e
decoder has access only to reconstructed pixel values ,
since the process of quantization of differential image introduces error,
reconstructed values, as expeceted diverges from the original values.
Identical predictions of both receiver and transmitter are assured by
transmitter configuration in which transmitter bases its prediction on the
same values as receiver i.e predicted values. The facts that were mentioned in
this paragraph are applicable to signals in general not just image and video
signals. Design of DPCM system means optimizing the predictor and quantizer
components, because the quantizer is included in prediction loop there is
complex dependancy between the prediction error and quantizaton error so joint
optimization should be performed to assure optimal results. But, modeling such
optimization is very complex so optimization of those two components are
usually optimized separately. It has been shown that under the mean-squared
error optimization criterion, apart constructions of quantizatior and
predictor are good approximations of joint optimization. Same as in the
previous paragraph, facts in this paragraph are also applicable to signals in
general. Delta modulation (DM )is a subclass of differential pulse
code modulation. It can be viewed as a simplified variant of DPCM, in which
1-bit quantizer is used with the fixed first order predictor, and was
developed for voice telephony applications. Input signal
is compared to the integrated output
and delta signal
(difference between the input signal and the pulse signal) is brought to
quantizer. Quantizer generates output
according to difference signal
if difference signal is positive quantizer generates positive impulse, and if
the difference is negative quantizer generates negative signal. So, output
signal
contains bipolar pulses. A typical example of a signal good for DPCM is a line in a continuous-tone
(photographic) image which mostly contains smooth
tone transitions. Another example would be an audio
signal with a low-biased frequency spectrum. For illustration, we present two histograms made from the same picture
which were coded in two ways. The histograms show the PCM and DPCM sample
frequencies, respectively. On the first histogram(Fig 4.), a large number
of samples has a significant frequency and we cannot pick only a few of them
which would be assigned shorter code words to achieve compression. On the second
histogram(Fig 5.), practically all the samples are between -20 and +20,
so we can assign short code words to them and achieve a solid compression
rate. Fig 4. Histogram of PCM sampled image Fig 5. Histogram of DPCM sampled image In practice, DPCM is usually used with lossy compression techniques, like
coarser quantization of differences can be used, which leads to shorter code
words. This is used in JPEG and in adaptive DPCM (ADPCM), a common audio
compression method. ADPCM can be watched as a superset of DPCM. |