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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)
P
Predictor used in the below example
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
N
0
1
Edge->2
3
4
5
u(n)
100
102
120
120
120
118
u(n)
0
100
101
106
111
116
e(n)
0
2
19
14
9
2
DPCM
e*(n)
0
1
5
5
5
1
u*(n)
100
101
106
111
116
117
Error u(n)
0
1
14
9
4
1
u(n)
0
100
102
120
120
120
Feedforward Predictive Coder
e(n)
e*(n) u*(n) Error u(n)
0
0
100
0
2
1
101
1
18
5
106
14
0
-1
105
15
0
-1
104
16
-2
-5
99
19
Q
u(n)
e(n)
Feed Forward
e*(n)
Q
u*(n)
Fig 11.6 a
P
u(n)
P
u*(n)
Feed Forward
u(n)
e(n)
e*(n)
e*(n)
u*(n)
Q
u*(n)
u*(n)
DPCM
P
P
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 pair. The transmitted co-efficients are shown below.
TYPICAL 8x8 VIDEO BLOCK
338
231
351
234
340
239
345
215
244
336
251
339
241
340
243
323
236
354
240
346
234
348
227
339
339
245
342
247
341
252
329
233
357
232
358
243
351
235
342
213
259
342
252
349
245
328
232
324
244
359
242
354
230
332
207
342
348
251
346
246
337
229
321
234
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
2
Of the 2D (NxN) DFT coefficients (N - 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
n
c
a
b
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
VLC
P
Xp(n)
Correlation:
M−k
Rxx(k)
=
1
M −k
xixi+k
_ (11.35)
i=1
X1
X2
X3
X4
X5
X6
X7
X8
M−1
Rxx(1)
=
1
M −1
xixi+k
i=1
=
1
(X1 X2 + X2 X3 + X3 X4 +.... + XM-1 XM)
M - 1
M−2
Rxx(2)
=
1
M −2
xixi+k
i=1
XM-4 XM-3 XM-2
XM-1
XM
=
1
(X1 X3 + X2 X4 + X3 X5 +.... + XM-2 XM)
M - 2
M−3
Rxx(3)
=
1
M −3
x ixi+k
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.