The document discusses DCT/IDCT concepts and applications. It provides an introduction to DCT and IDCT, explaining that they are used widely in video and audio compression. It describes the DCT and IDCT functions and how they work to transform signals between spatial and frequency domains. Examples of one-dimensional and two-dimensional DCT/IDCT equations are also given. Finally, common applications of DCT/IDCT compression techniques are listed, such as in DVD players, cable TV, graphics cards, and medical imaging systems.

1. ®
The DCT/IDCT Solution
Customer Tutorial
February 2000
File Number Here

2. Agenda
Introduction
DCT/IDCT Concepts
DCT/IDCT Applications
Spartan-II DCT/IDCT IP Solutions
Summary
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3. Introduction
Spartan-II FPGAs
— 100,000 System Gates at under $10
— Extensive features: Block RAM, DLL, Select I/O
— Vast IP Portfolio
— Provide Density, Features, Performance at ASIC prices
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4. DCT/IDCT Compression
Compression allows increased throughput through
transmission medium
— Video and audio compression makes multimedia systems very
efficient
– Increases CPU bandwidth
– Higher video frame rates
– Better audio quality
– Enables multimedia interactivity
DCT and IDCT are widely used in video and audio
compression
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5. DCT/IDCT Overview
DCT - Discrete Cosine Transform
IDCT -Inverse Discrete Cosine Transform
®

6. DCT/IDCT Concept
What is DCT?
— X= DCT(video/audio input)
– Returns the discrete cosine transform of ‘video/audio input’
– Can be referred to as the even part of the Fourier series
– Converts an image or audio block into it’s equivalent frequency
coefficients
What is IDCT?
— The IDCT function is the inverse of the DCT function
— The IDCT reconstructs a sequence from its discrete cosine
transform (DCT) coefficients
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7. DCT/IDCT Concept
The DCT transform of an image brings out a set of
numbers called coefficients.
A coefficient’s usefulness is determined by its variance
over a set of images as in video’s case.
If a coefficient has a lot of variance over a set, then it
cannot be removed without affecting the picture quality.
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8. DCT/IDCT Concept
DCT
Frequency
Coefficients
Compared to
Magnitude
Original Image Thresholds
Resulting in
Compressed
IDCT Data Streams
The image is broken into 8x8
groups, each containing 64
pixels. Three of these 8x8
groups are enlarged in this
Recovered Image
figure, showing the values of
(Notice Lesser Image Quality) the individual pixels, a single
byte value between 0 and 255.
Courtesy: The Scientist and Engineer's Guide to Digital Signal Processing by Steven W. Smith
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9. DCT/IDCT Concept
Divide picture into
16 by 16 blocks.
(macroblocks) Each block is 8
pixels by 8 lines.
Each macroblock is
16 pixels by 16 lines.
(4 blocks)
DCT
8 X 8 Block Frequency
Coefficients
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10. DCT/IDCT Usage
Areas of Use:
— One-Dimensional DCT/IDCT
– Dolby AC2 & AC3
– Biomedical signals like EEG & ECG
– Speech information compression
— Two-Dimensional DCT/IDCT
– JPEG Encoders
– MPEG-1 & MPEG-2
– Image & Pattern Recognition
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11. DCT/IDCT Concept
One-Dimensional DCT Equation
N-1
Xc(k) = (1/N) Σ xn cos(k2πn/N),
n=0
where
k = 0, 1, 2, …, N-1
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12. DCT/IDCT Concept
One-Dimensional IDCT Equation
N-1
xc(k) = Σ c[u] Xn cos(k2πn/N),
n=0
where
k = 0, 1, 2, …, N-1,
Xn is the DCT result, and
c[u] = 1 for u=0, and c[u] = 2 for u=1,2,3,…N-1
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13. DCT/IDCT Concept
Two-Dimensional DCT Equation
N-1 N-1
F[u, v] = 1/N2 Σ Σ f[m, n] cos[ (2m + 1)uπ/ 2N] cos[ (2n + 1)vπ/2N ]
m=0 n=0
where:
u, v = discrete frequency variables (0, 1, 2, …, N - 1),
f[m, n] = N by N image pixels(0, 1, 2, …, N - 1), and
F[u, v] = the DCT result
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14. DCT/IDCT Concept
Two-Dimensional IDCT Equation
N-1 N-1
f[m, n] = Σ Σ c[u] c[v] F[u, v] cos[ (2m + 1)uπ/ 2N] cos[ (2n + 1)vπ/2N ]
m=0 n=0
where:
m, n = image result pixel indices( 0, 1, 2, …, N – 1 ),
F[u, v] = N by N DCT result,
c[λ] = 1 for λ=0 and c[λ]=2 for λ=1,2,3,…N-1
f[m, n] = N by N IDCT result
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15. DCT/IDCT Concept
Example of a Simplistic one-Dimensional DCT
— Data is transformed first and the newly calculated values are
threshold limited to a magnitude of 0.375
— Assuming a data sequence to be {1, 2, 0, 5}
Applying the one-Dimensional DCT formula,the resultant DCT
sequence is {2, 0.25, -6, 0.25}
The values that above the threshold (|values| > 0.375) are 2 and –6
This results in a 50% reduction in data size with minimal loss in
quality
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16. DCT/IDCT
Applications
®

17. DCT/IDCT Applications
List of Some End Applications
— DVD/Video CD Players
— Cable TV
— DBS Systems
— HDTV
— Graphics/Image Processing Cards
— Ultrasound/MRI Systems
— Digital VCRs
— Set-Top Boxes
— Digital Camera
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18. DCT/IDCT in JPEG
Encoding
Compressed
Zig-Zag Data
Pixel Data Coefficient Run-Length Huffman
DCT
Encoding Encoding
Quantization
Decoding Reconstructed
Compressed Huffman Zig-Zag Pixel Data
Run-Length Coefficient
Data Decoding IDCT
Expansion Denormalization
JPEG Codec Block Diagram
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19. DCT/IDCT in Bio-Medical
1-D DCT is commonly used on a sequence of digital
information like voice or heartbeat information in an ECG
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20. DCT/IDCT in DVD/VCD
Reconstructed (Decoded) Frame
Inverse
IDCT
Quantizer
Video to Coded Video
be Coded Bitstream Bitstream
DCT Quantizer Coder
+ -
Motion Motion
Estimator Compensator
Anchor Frame
Storage
Courtesy: C-Cube Corporation
MPEG-2 Block Diagram in a Typical DVD System
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21. DCT/IDCT in DVD/VCD
Master Variable Bit Rate or
Video Tape MPEG-2 Audio Encoder
Quality
Control
Multiplexing
Emulation
Human and Formatting
Assist Master
Recoding Disc
Master Dolby AC3 or
Audio Tape MPEG-2 Audio Encoder
Courtesy: C-Cube Corporation
DVD/VCD Mastering
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22. DCT/IDCT in DVD/VCD
Digital Audio/Video Decoder
MPEG-2 Video Decoder
NTSC/
PAL To TV
DVD Subpicture OSD Encoder
DSP DEMUX Processing Graphics
To Audio System
Dolby AC3 or
MPEG-2 Audio Decoder
Front Panel
Microcontroller 10:00:23 ||
Courtesy: C-Cube Corporation
DVD Player
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23. DCT/IDCT in DVD/VCD
DVD Players
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24. DCT/IDCT
in Digital Cameras
2-D DCT/IDCT is applied generally on data sets that have a
naturally two-dimensional characteristic, like a digital image
Digital Cameras
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25. Spartan-II DCT/IDCT
Solution
DCT/IDCT Cores
— Available Separately or Combined
AllianceCORE Xentec DCT/IDCT Core
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26. Spartan-II DCT/IDCT
Solution Features
Features Spartan-II
Device XC2S100-6
CLBs 1026
Clock IOBs 1
IOBs 28
Performance (MHz) 33.3
AllianceCORE Xentec DCT/IDCT Core
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27. Spartan-II DCT/IDCT
Solution Performance
Low cost Spartan-II FPGA with soft IP from Xentec has
High Performance
— 180 times faster 32-bit mainstream processor operating at
266MHz
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28. Spartan-II DCT/IDCT
Solution - Features
The Xilinx solution is efficient and cost-effective compared
to DCT/IDCT software solution being run by a high
performance 32-bit processor
The Xilinx Xentec core solution is capable of operating
either as DCT or IDCT by the use of a single mode pin
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29. Summary
DCT/IDCT Solutions are Widely Used in Multimedia,
Video, Audio, and Imaging Applications
The Spartan-II Family has Significant Strengths in its
DCT/IDCT Solution:
— Features
— Performance
— Scalability and Flexibility
— Cost effectiveness
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