1. :: Discrete Cosine Transformation
Tommy Taylor
Brandon Hsiung
Changshi Xiao
Bongkwan Kim
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2. ::welcome Discrete Cosine Transformation
Boring math leads to great applications:
MPEG2, DVD, HDTV, MP3
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3. ::Application An image codec example (JPEG) : DCT Quant.
Huffman encoding
Storage/
transmission channel
IDCT
deQuant.
Huffman decoding
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4. ::2D DCT Definition
Xm,n=(C(m)C(n)/4)*i=0,7 j=0,7xi,jcos((2i+1)m/16)cos((2j+1)n /16)
Where C(m),C(n) are constants:
C(n) = /sqrt(2) , if n = 0
or 1 , if n  0
It can be decomposed into two 1D DCT, first apply on rows , then on columns. 1D DCT is defined as :
Xn = (C(n)/4)*i=0,7 xicos((2i+1)n/16)
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5. ::Fast Algorithm of 1D DCT
A A A A
A C -A -B
A -C -A B
A -B B -C
D E F G
E -G -D -F
F -D -G E
G -F E -D
x0 + x7
x1 + x6
x2 + x5
x3 + x4 X0 X2 X4 X6
x0 - x7
x1 - x6
x2 - x5
x3 - x4 X1 X3 X5 X7 =
A = cos(/4)
B = cos(/8)
C = sin(/8)
D = cos(/16)
E = cos(3/16)
F = sin(3/16)
G = sin(/16)
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6. This is what we’re going to do !
::2D DCT Architecture
Data in
This is what we’re going to do !
1D DCT (on rows)
Transpose RAM
1D DCT (on columns)
Data out
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7. + -  1D DCT : direct implementation, none real time processing R0
Selector R1 R2 R3 R4 R5 R6 R7 + - R8 R9 
R10
R12
R13
Parallel to serial
Control
logic
ROM
R11
in_data(16)
in_valid
out_valid
out_ready
out_done
clk
vdd
vss
reset
out_data(16)
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8. -  + 1D DCT : parallel architecture for real time processing R0 R1 R2
Selector
R16 +
R20
Parallel to serial
Control
logic
ROM
R17 - R8 R9
R10
R11
R12
R13
R14
R15 
R22
R18
R21
R19
R23
in_data(16)
clk
vdd
vss
out_done
out_data(16)
in_run
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9. ::Transistor Estimate
architecture
Adder
Multiplier
register
ROM
control
total
pins A1
4x16x30
2 x 4000
14x16x20
7x16
1000
15512 40 A2
12x16x30
4 x 4000
24x16x20
14x16
30664 37
architecture
latency
throughput
Real time
Clock A1
14 cycle
2samples /6 cycle No ? A2
12 cycle
1 sample/cycle
Yes
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10. ::Design Goals High throughput, real time, 1sample/clock
Clock rate, MHz (for HDTV applications)
Area, ~30k, can we afford it ???
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11. :: Secondary Ideas Motion Prediction for DVD-Video Serpent Encryption
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12. ::conclusion & questions
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