Companding and DPCM and ADPCM by Naimish Patel

2. Prepared by: Naimish Patel

3. COMPANDING
 Companding is non uniform quantization. It is required to be implemented to improve the signal to
quantization noise ratio of weak signals. We know that the quantization noise is given by
Nq = (Δ^2)/ 12
 This shows that in the uniform quantization , once the step size is fixed, the quantization noise power
remains constant. However, the signal power is not constant. It is proportional to the square of signal
amplitude.
 Hence signal power will be small for weak signals, but quantization noise power is constant.
Therefore, the signal to quantization noise for weak signals is very poor. This will affect the quality of
signal. The remedy is to use COMPANDING.
 COMPANDIND is a term derived from two words i.e., COMPRESSION and EXPANTION.
Companding = Compressing + Expanding
 In practice, it is difficult to implement the non-uniform quantization because it is not known in
advance about the changes in the signal level. Therefore, a particular method is used.

4. • The weak signals are amplified and strong signals are attenuated before applying them to a uniform
quantizer. This process is called as COMPRESSION and the block that provides it is called as a
COMPRESSOR.
( A companding model )
 At the receiver exactly opposite is followed which is called expansion. The circuit used for providing
expansion is called as an EXPANDER. The compression of signal at the transmitter and expansion at
the receiver is combined to be called COMPANDING. The process of companding has been shown in
the form of a block diagram in below figure.

5. 1.COMPRESSOR CHARACTERISTIC
 This figure shows the compressor
characteristics. As shown in the
figure provides a higher gain to the
week signals and smaller gain to the
strong input signals.
• Thus, weak signals are artificially boosted to
improve the signal to quantization
noise ratio.
• It may be noted that this
compressor characteristics has been
shown only for the positive input
signal but we can draw it even for
the negative input signals using the
some principle.
• In fact, the compressor is induced at the PCM
transmitter.

6. 2.EXPANDER CHARACTERISTICS
 Figure shows the expander
characteristics. This characteristics
is exactly the inverse of the
compressor characteristics.
 This ensures that all artificially boosted
signals by the compressor are
brought back to their original
amplitudes at the receiver end.

7. 3.COMPANDER CHARACTERISTIC
 Figure shows the compander characteristics
which is the combination of the compressor
and expander characteristics.
 Due to the inverse nature of compressor and
expander, the overall characteristics of the
compander is a straight line.

8. DIFFERENT TYPES OF COMPRESSION CHARACTERISTICS
 Ideally, we need a linear compressor characteristics for small amplitudes of the input signal
and a logarithmic characteristic elsewhere. In pratice, this is achieved by using following
two methods:
( i ) μ-law companding
( ii ) A-law companding
 μ -LAW COMPANDING :
 In the μ-law companding, the compressor characteristic is continuous. It is approximately
linear for smaller values of input levels and logarithmic for high input levels.
 The practically used the value of μ is 255. It may be noted that the characteristic
corresponding to μ = 0 corresponds to the uniform quantization.
• The μ-law companding is used for speech and must signals. It is used for PCM telephone
systems in United states, Canada and Japan.

9. Figure shows the variation of signal to quantization noise
ratio with respect to signal level. It is obvious that SNR
is almost constant at all the signal levels when
companding is used.
The μ-law compressor characteristic is mathematically
expressed under:

10.  A -LAW COMPANDING :
• In the A-law companding, the compressor characteristic is
piecewise, made up of a linear segment for low level
inputs and a logarithmic segment for high level inputs.
• A-law companding is used for PCM telephone system in
Europe.

11. DPCM (DIFFERENTIAL PULSE CODE MODULATION)
 PCM is not a vary efficient system because it generates so many bits and requires so much bandwidth
to transmit. Many different ideas have been proposed to improve the encoding efficiency of A/D
conversion. In general, these ideas exploit the characteristics of the source signals. DPCM is one such
scheme.
 In analog message we can make a good guess about a sample value from knowledge of past sample
values.
 Consider a simple scheme; instead of transmitting the sample values, we transmit the difference
between the successive sample values. Thus, if m[k] is the kth sample, instead of transmitting m[k],
we transmit the difference
d[k] = m[k] + m[ k-1 ].
 At the receiver, knowing d[k] and several previous sample value m[ k-1 ], we can reconstruct m[k].
Thus, from knowledge of the difference d[k], we can reconstruct m[k] iteratively at the receiver. Now,
the difference between successive samples is generally much smaller then the sample values. Thus,
the peak amplitude (mp) of the transmitted values is reduced considerably.

12.  Because the quantization interval Δv = mp / L, for a given L ,this reduce the quantization
interval Δv, Thus reducing the quantization noise, which is given by Δv^2 / 12.
 This means that for given n, we can increase the SNR, or for a given SNR, we can reduced n.
• We can improve upon this scheme by estimating (predicting) the value of the kth sample m[k]
from a knowledge of several previous sample values.
• If this estimate is m̂ [k], than we transmit the difference (predication error) d[k] = m[k] –
m̂ [k].
• At the receiver also, we determine the estimate m̂ [k] from the previous sample values, and
than generate m[k] by adding the received d[k] to the estimate m̂ [k]. Thus, we reconstruct the
samples at the receiver interatively.
• If our prediction is worth its salt, the predicated value m̂ [k] will be close to m[k], and their
difference (prediction error) d[k] will be even smaller than the difference between the
successive samples. Consequently this scheme, known as the DPCM.

13. ROLE OF PREDICTOR
• It is observe that if the sampling takes place at a rate which is higher then the Nyquist rate, then there
is a correlation between successive samples of the signal m[k].
• Hence a knowledge of past sample values or difference helps us to predict the range of next required
increment or decrement at the predictor output.
• This reduced the difference or error between m[k] and m̂ [k]. Therefore to encode this small value of
error the DPCM system requires less number of bits which will reduce the bit rate. This is the role of
predictor in DPCM system.

14. (Linear predictor block diagram)
• Linear predicted equation: m̂ [k] = a1m[ k-1 ] + a2m[ k-2 ] + …………. + aN m[ k-N ]
• This is the equation of Nth –order predictor. Larger N would result in better prediction in general. The
output of this filter is m̂ [k]. The predictor described in above equation is called a Linear Predictor.

15. ANALYSIS OF DPCM
• In DPCM we transmit not the present sample m[k], but d[k] (the difference between m[k] and its predicated
value m̂ [k]).
•At the receiver, we generate m̂ [k] from the past sample values to which the received d[k] is added to
generate m[k].
• There is, however, one difficulty associated with the scheme. At the receiver, instead of the past samples m[
k-1 ], m[ k-2 ], ....., as well as d[k].
•we have their quantized versions mq [ k-1 ], mq [ k-2 ], ..... Hence, we can not determine m̂ [k].

16. (DPCM transmitter)
 We can determine m̂ q[k], the estimate of the quantized sample mq[k], in terms of the
quantized samples mq [ k-1 ], mq [ k-2 ], ..... This will increase the error the
reconstruction.

17.  In such a case, a better strategy is to determine m̂ q[k], the estimate of mq[k], at the transmitter also
from the quantized samples mq [ k-1 ], mq [ k-2 ], ..... The difference d[k] = m[k] - m̂ q[k] is now
transmitted via PCM. At the receiver, we can generate m̂ q[k], and from the received d[k], we can
reconstruct mq[k].
 Figure shows a DPCM transmitter. We shell soon so that the predicator input is mq[k]. Naturally, it’s
output is m̂ q[k], the predicted value of mq[k]. The difference
d[k] = m[k] - m̂ q[k]
is quantized to yield
dq[k] = d[k] + q[k]
• Where q[k] is quantization error. The predicted output m̂ q[k] is feedback to its input so that the
predictor input mq[k] is
mq[k] = m̂ q[k] + dq[k]
= m[k] – d[k] + dq[k]
=m[k] + q[k]

18. (DPCM receiver)
 This shows that mq[k] is quantized version of m[k]. The predictor input is indeed mq[k], we assumed.
The quantized signal dq[k] is now transmitted over the channel.

19.  The receiver shown in figure is identical to the shaded portion of the transmitter. The
inputs in both cases are also the same, namely dq[k]. Therefore, the predicted output must
be m̂ q[k] (the same as the predictor output at the transmitter).
 Hence, the receiver output (which is the predictor input) is also the same, viz., mq[k] =
m[k] + q[k], as found in equation. This shows that we are able to receive the desired
signal m[k] plus the quantization noise q[k].
 This is the quantization noise associated with difference signal d[k], which is generally
much smaller then m[k]. The received samples mq[k] are decoded and passed through a
low-pass filter for D/A conversion.

20. • ADVANTAGE OF DPPCM
• As the difference between m[k] and m̂ [k] is being encoded and transmitted by the PCM technique, a
small difference voltage is to be quantized and encoded.
• This will need less number of quantization levels and hence less number of bits to represent them.
• Thus signalling rate and bandwidth of a DPCM system will be less than that of PCM.
• DISADVANTAGE OF DPCM
• High bit rate
• Needs the predictor circuit to be used which is very complex.
• Practical usage is limited.

21. SNR IMPROVEMENT:
• To determine the improvement in DPCM over PCM, let mp and dp be the peak amplitudes of m(t) and
d(t), respectively.
• If we use same value of L in both the cases, the quantization step in DPCM reduced by the factor .
• Because the quantization power is (Δv)^2 / 12, the quantization noise in DPCM is reduced by the
factor (mp / dp )^2 , and the SNR is increased by the same factor.
• Where pm and pd are the powers of m(t) and d(t), respectively.
• In terms of decibel units, this means that SNR increases by 10log( Pm / Pd )dB. Therefore the value of
α is higher by 10log( Pm / Pd )dB.

22. ADPCM (ADAPTIVE DIFFERENTIAL PLUSE CODE MODULATION)
• Adaptive differential plus code modulation can further improve the efficiency of DPCM encoding by
incorporating an adaptive quantizer at the encoder.
(Block diagram of ADCM)

23. • Figure illustrates the basic configuration of ADPCM. The number of quantization level L is
fixed. When a fixed quantization step Δv is applied, either the quantization error is too large
because Δv is too big or the quantizer cannot cover the necessary signal range when Δv is too
small.
• Therefore, it would be better for the quantization step Δv to be adaptive so that Δv is large or
small depending on whether the prediction error quantizing is large or small.
• It is important to note that the quantized prediction error can be good indicator of the
prediction error size.

24.  APLLICATIONS:
 ADPCM speech coder and decoder (codec )
 ADPCM codec are used in the personal handyphone systems ( PHS ) or personal access system (
PAS ).
The PHS is a mobile network system similar to a cellular network. It is a short range low power
facility and operates in the 1880 to 1930 MHz frequency band.

25. Thank You