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out e*(n)

5

1

-6 -4 -2 0 2 4 6 e(n)

-1

-5

Fig 11.7: Quantizer used in the below example

e*(n) u*(n) u(n) Predictor used in the below example

P




The sequence 100,102,120,120,120,118,116 is to be predictively coded using the previous element prediction rule u*(n) = u*(n-1) for DPCM and u(n) = u(n-1) for feed forward predictive coder. Assume a 2-bit quantizer shown in fig 11.7. Only the firsts ample is quantized separately by a 7 bit uniform quantizer giving u*(0) = u(0) = 100. The following table shows how reconstruction error builds up with a feed forward predictive coder whereas it tends to stabilize with the feedback system of DPCM. Reconstruction error = u(n) – u*(n) Input DPCM Feedforward Predictive Coder N u(n) u(n) e(n) e*(n) u*(n) Error u(n) u(n) e(n) e*(n) u*(n) Error u(n) 0 100 0 0 0 100 0 0 0 0 100 0 1 102 100 2 1 101 1 100 2 1 101 1 Edge->2 120 101 19 5 106 14 102 18 5 106 14 3 120 106 14 5 111 9 120 0 -1 105 15 4 120 111 9 5 116 4 120 0 -1 104 16 5 118 116 2 1 117 1 120 -2 -5 99 19 Q u(n) e(n) Q e*(n) u*(n)

Feed Forward Fig 11.6 a

u(n) u*(n)

Feed Forward

u(n) e(n) e*(n) e*(n) u*(n)

u*(n) u*(n)

DPCM

The 2 dimentional 8x8 transform may be obtained by transforming each horizontal line of the 8x8 block independetly with the N=8 and then transforming each of the column of the resulting 8x8 block independently in the vertical direction. A typical input and its resulting transform follows. Since the 64 elements of the input matrix are all real numbers the output matrix will consists of four real coefficients and 30 complex conjugate pairs. One complex coefficient must be saved from each complex conjugate pairs. The transmitted co efficient are shown below.

TYPICAL 8x8 VIDEO BLOCK

338 244 236 339 357 259 244 348 231 336 354 245 232 342 359 251 351 251 240 342 358 252 242 346 234 339 346 247 243 349 354 246 340 241 234 341 351 245 230 337 239 340 348 252 235 328 332 229 345 243 227 329 342 232 207 321 215 323 339 233 213 324 342 234

P P

Q

P P




8x8 unitary DFT of the above video

231, 8 -7, -2 -1,-1 -2, 2 0, 0 -2,-2 -1, 1 -7, 2

-2,-33 12, 10 -8, 5 -2, 4 -1, 0 -2, 1 -8, 4 -9, -5

7, -9 -11, 5 -4, -1 -2, -1 -2, -2 -1, -2 -5, -5 1, -7

14, 1 -2, 0 3, -5 1, 0 0, 1 -2, 1 7, 1 -4, 0

1, 0 -3, 0 232,185 -5, 4 3, 0 -5, -4 232, -185 -3, 0

14, -1 -4, 0 7, -1 -2, -1 0, -1 1, 0 3, 5 -2, 0

7, 9 1, 7 -6, 4 -1, 2 -3, 2 -2, 1 -4, 0 -11, -5

-2, 33 -9, 5 -8, -4 -2, -1 -1 , 0 -2, -4 -8, -5 12, -10

Of the 2D (NxN) DFT coefficients (N2- 4)/2 coefficients are complex and 4 are real . These are independent (unique). DS- 3(44.736 Mbps) NTSC TV Video codec developed by Grass Valley Corp GrassValley, CA. Temporal DPCM Quantized 2D DFT Coefficients are substracted from corresponding coefficients of the previous frame to generate temporal DPCM no of bits to encode the TDPCM output is compared with that for Quantized 2D DFT coefficients and a decision is made on a block – by – block basis which of the two modes are to be sent to the decoder. The DS- 3(44.736 Mbps) coder proposed to T1.Y1.1 by NEC (Japanese company) chooses one of the following four properties (Fig 11.9). DPCM is applied to composite color TV signal (NTSC) sampled at 3 fSC where fSC is the color sub carrier frequency, 3.57 MHz

fS = 3 x 3.57MHz = 10.71 MHz

Predictor Number Previous pixel prediction

1 x = a

2 x = 0.5a + c -0.5d (Higher order DPCM)

3 x = e (Two Line Delay)

4 x = f (One field Delay)

Fig 11.9

JPEG (Joint Photographic Experts Group) still frame continuous – tone Image compression. ISO/IEC, JTC1/SC29 adopted by ITU-T as T.81 is part1 Predictor selection indicated by header at the start of the frame n-1 c b n a x under prediction xp = a b c a + b - c a + ( b – c )/2 b + (a - c)/2 (a + b)/2 LOSSLESS SYSTEM Predicted value




x(n) ep(n) Arithmetic or Huffman Coder Xp(n)

VLC

P




Correlation: M−k

Rxx(k) = 1 xixi+k _ (11.35) M −k i=1 X1 X2 X3 X4 X5 X6 X7 X8 XM-4 XM-3 XM-2 XM-1 XM

M−1 Rxx(1) = 1 xixi+k M −1 i=1

= 1 (X1 X2 + X2 X3 + X3 X4 +.... + XM-1 XM)

M - 1

M−2 Rxx(2) = 1 xixi+k M −2 i=1




= 1 (X1 X3 + X2 X4 + X3 X5 +.... + XM-2 XM)

M - 2

M−3 Rxx(3) = 1 xixi+k M −3 i=1

= 1 (X1 X4 + X2 X5 + X3 X6 +.... + XM-3 XM)

M – 3

(Correlation with 3 samples apart)

DPCM Design:




N = 1, a1 = 0.66

N = 2, a2 = 0.096, a1 = 0.596

N = 3, a3 = 0.577, a2 = -0.025, a1 = 0.204

Based On:

[A] = [a1, a2, ……., an]T

SPER: Signal to Prediction error

Uniform Quantizer Laplacian




Note: Directly quantize the speech input See fig 11.9 for reconstructed speech sequence dn Out

(No zero output level)

8 level uniform quantizer In When dn is small dn cap flipps between the two inner levels leading to hissing sound

Inner levels

dn = Prediction error

a1 = 0.577, a2 = -0.025, a3 = 0.204

3rd order predictor, 8 levels, uniform quantizer, Laplacian pdf (step size = 0.5) – Fig 11.7




Samples #s (700 – 2000) (2200 – 3500) 11.5 Adaptive DPCM Forward adaptive - (based on previous original / input samples, X n+k ), adaptive predictor info (predictor weights) need to be transmitted to the receiver as side information. Backward adaptive – ( based on X n-k ), which is available at the receiver. No side information. Use adaptive quantizers. P.S. All Figures/Tables etc., are from K.Sayood, “Introduction to Data Compression”, 3rd edition, Morgan Kauffman, 2006.




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