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Explain DPCM and ADPCM techniques used in audio compression.
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DPCM (Differential Pulse Code Modulation)

i. Adjacent audio samples tend to be similar in much the same way that neighboring pixels in an image tend to have similar colours.

ii. The simplest way to exploit this redundancy is to subtract adjacent samples and code the differences, which tend to be small integers. Any audio compression method on this principle is called DPCM

iii. A block diagram of DPCM is shown below:

Fig2.5.a Encoder

Fig2.5.a Encoder

Figure 2.5.b Decoder

Figure 2.5.b Decoder

iv. The DPCM system consists of two major components predictor and quantizer.

v. DPCM gains its advantage by the reduction in variance.

vi. Variance is reduced on how well the predictor can predict the next symbol based on past reconstructed symbols.

vii.

  • The variance in above is given by:

    σd2=E[(XnPn)2]

  • The reconstructed sequence is given by :

    Xn =Xn+qn

  • The predictor sequence {Pn } is given by:

    Pn=f{X  n1,X  n2,,X  0}

  • Assume quantizer value to be small that replace Xn   by  Xn

    Pn=f(Xn1,Xn2,,X0)

  • Assume predictor to be linear

    Pn=1.X  n1

  • Variance is given by….

    σ2a=E[(xnNi=1ai.xn1)2]=0δσ2aa1=2E[(xnNi=1ai.xn1)xn1]=0δσ2aa2=2E[(xnNi=1ai.xn1)xn2]=0δσ2aaN=2E[(xnNi=1ai.xn1)xnN]=0

    Taking the expectations, we can rewrite there equations as:

Ni=rai.Rxx(i1)=Rxx(1)Ni=1ai.Rxx(i2)=Rxx(2)..Ni=1ai.Rxx(iN)=Rxx(N)

In matrix form RA=P

Where

R=[ RxxRxxx(1)Rxx(2)........Rxx(N1) Rxx(N1)...........Rxx(0)]

A=[ a1 a2 .... aN]and  P=[ Rxx(1) Rxx(2) .... Rxx(N)]

  • These equations are known as discrete form of weiner- hopf equation
  • If we know autocorrelation RXX(k)fork=0,1,.N
  • We can find predicta coefficients

    A=R1P

    [

    DPCM

  • x = [8.5, 9.3, 6.6, 4.5, 7.8] -> Output Sampling
  • x^ = [9 , 9 , 7 , 5, 8 ] -> Output Quantizer
  • x^ = [9 , 0, 2 , 2 ,-3] -> Output DPCM
  • r^ = [ 9 , 0 ,2 , 2. -3] -> Received Input
  • r = [ 9, 9, 7, 5, 8] -> Differential Output

    ]

ADPCM (Adaptive Differential Pulse Code Modulation)

i. Compression is possible only because sound and thus audio samples tend to have redundancies.

Disadvantages of DPCM:

ii. In DPCM we subtract adjacent samples and code the differences, however this method is inefficient since they do not adapt themselves to varying magnitudes of audio stream.

iii. Hence, better results are obtained using ADPCM (Adaptive Differential Pulse Code Modulation).

iv. ADPCM uses the previous sample to predict the current sample.

v. It then computes the difference between the current sample and its predictions and quantizes the difference.

Figure 2.6.a ADPCM Encoder

Figure 2.6.a ADPCM Encoder

vi. The adaptive quantizer receives the difference D (n) between the current input sample x [n] and predictor Xp[n1]

vii. The quantizer computes and outputs the quantized code C [n] of X [n].

viii. The same code is sent to adaptive dequantizer (some dequantizer is used by the decoder) which produces the next quantized difference value DP[n].

ix. This value is added to previous predictor value Xp[n1] and sum Xp[n] is sent to the predictors to the used in next stop.

Figure 2.6.b ADPCM Decoder

Figure 2.6.b ADPCM Decoder

x. Its input is code c(n) , dequantizes it is to a difference Dq[n] , which is added to preceeding predictor output Xp[n1] to form next output Xp[n]

xi. The next output is also fed into predictor to be used in next step.

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