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Digital Representations

Digital Representations. Digital Video Special Effects Fall 2006. Analog-to-Digital (A-D) Conversion. Sampling Quantization Coding. Sampling -- Analog to Discrete. Analog signal to discrete-time signal x ( t ) --> x [ n ] Sampling procedure f ( t ) is the sampling function

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Digital Representations

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  1. Digital Representations Digital Video Special Effects Fall 2006

  2. Analog-to-Digital (A-D) Conversion • Sampling • Quantization • Coding

  3. Sampling -- Analog to Discrete • Analog signal to discrete-time signal • x(t) --> x[n] • Sampling procedure • f(t) is the sampling function • Simple sampling • x[n] = x(t=n), i.e., f(t)=d(t)

  4. Reconstruction: Discrete to Analog • Can we reconstruct analog signal from its discrete time samples? • x[n] --> x(t) ? Generally not. • Nyquist (Shannon) sampling theorem for bandlimited signals • If the simple sampling rate is at least twice bandwidth of the analog signal, the analog signal can be perfectly reconstructed:

  5. Quantization -- Digitization • Discrete-time signal  digital signal • Quantization error • Quantization level • How many bits to represent one sample? • Trade-off between error and bit rate (communication band width) • Nonlinear quantization • Pre-compression and de-compression (m law and A law) • Vector quantization

  6. Raw Data Rate • Sampling frequency= f (Hz) • Each sample represented by R bits • Raw data rate (bit rate): T = f x R (bits per second, or bps)

  7. Digital Audio Signals • Frequency band of sound: human hearing frequency range: 20Hz-20 KHz. • Sampling rate > 40 KHz (Actual sampling rate of CD-Audio = 44.1 KHz) • Bit rate for CD quality audio signal (44.1 KHz, Quantization:16 bits, 2 channels):T = 44100 x 16 x 2 (bits per second, or bps) • CD quality stereo sound  10.6 MB / min

  8. Examples

  9. Speech Signals • Properties • Human ear: most sensitive to 600Hz-6000Hz • Quasi-stationary for around 30 ms • Characteristic maxima -- formants • Speech analysis and synthesis • Speech components, e.g., vowels and consonants

  10. MIDI • A protocol that enables computer, synthesizers, keyboards, and other musical device to communicate with each other. • Bit rate: 31.25Kbps • A MIDI file stores the messages regardingspecific musical actions. • Commands, instead of actual waveforms, are saved. • One minute of MIDI: 4KB storage.

  11. Digital Image Representation • Picture elements (pixels) • Sampling, quantization • Higher dimensional image -- voxels • Bi-level images (black/0 or white/1) • Grayscale images • 1 byte/pixel: 256 gray levels • Color images • True color: RGB 24bits/pixel • Image size, e.g. VGA 640x480 • Grayscale image: 307,200 bytes • True color image: 921,600 bytes

  12. Graphics Format • Graphics primitives and attributes • 2-D objects: lines, rectangles, circles, ellipses, text strings, etc. • Attributes: line style, line width, color, etc. • High-level representation: structured, object-based • Low-level representation: bitmap

  13. Computer Graphics • Computer animation • Computer Generated Images (CGI) • Photo-realistic rendering

  14. Video Signal Requirements • Aspect ratio: TV  4/3; HDTV16/9 • Luminance and chrominance • Continuity of motion > 15 frames/s • TV 30 or 25 frames/s, movie 24 frames/s • Flicker. Marginal at least 50 refresh cycles/s • Movie: 2x24=48 • TV: Half picture by line-interleaving • Scanning rate: at lease 25Hz, finish one frame in 1/25s

  15. Color Representation in Video • RGB, normalized R=G=B=1 -- white color • YUV signal • Y=0.30R+0.59G+0.11B (Luminance) • U=(B-Y) x 0.493, V=(R-Y) x 0.877 (Chrominance channels) • Example: PAL, CD-I and DVI (Digital Video Interactive) video. • YIQ signal • Y=0.30R+0.59G+0.11B (Luminance) • I=0.60R-0.28G-0.32B, Q=0.21R-0.52G+0.31B • Example: NTSC • Avoid cross talk between luminance and colors: S-Video video signals separate the luminance and chrominance information into two separate analog signals.

  16. Subsampling in Video • Different spatial sampling rates for different chrominance channels • Human beings are more sensitive to luminance (using more samples) while less sensitive to colors (using less samples). • Different resolution for different components • Y:C1:C2 -- 4:2:2 • Subsampling and upsampling techniques

  17. Computer Video Format • CGA (Color Graphics Adapter): 4 colors, 320x200x2bits = 16,000 bytes • EGA: 640x350x4bits = 112,000 bytes • VGA: 640x480x8bits = 307,000 bytes • SVGA: 800x600 pixels • XGA: 1024x768 pixels • SXGA: 1280x1024 pixels

  18. Video Quality • VCR Quality -- SIF (MPEG1) • NTSC: 240x352; PAL: 288x352 per frame • Videoconferencing quality • CIF (Common Interchange Format) -- H.261 • 288x352, subsampling 4:1:1(halving both direction) • Q: what is the raw bit rate of CIF video (30frames/s)? • QCIF (Quarter CIF) • 144x176, subsampling 4:1:1(halving both direction) • Q: what is the raw bit rate of QCIF video (30frames/s) • Super-CIF: • 576x704, subsampling 4:1:1(halving both direction)

  19. The Need for Compression • Take, for example, a video signal with resolution 320x240 and 256 (8 bits) colors,30 frames per second • Raw bit rate = 320x240x8x30 = 18,432,000 bits = 2,304,000 bytes = 2.3 MB • A 90 minute movie would take 2.3x60x90 MB = 12.44 GB • Without compression, data storage and transmission would pose serious problems!

  20. Data Compression • Data compression requires the identification and extraction of source redundancy. • In other words, data compression seeks to reduce the number of bits used to store or transmit information.

  21. Lossless Compression • Lossless compression can recover the exact original data after compression. • It is used mainly for compressing database records, spreadsheets or word processing files, where exact replication of the original is essential. • Examples: Run Length Encoding (RLE), Lempel Ziv Welch (LZW), Huffman Coding.

  22. Lossy Compression • Result in a certain loss of accuracy in exchange for a substantial increase in compression. • More effective when used to compress images and voice where losses outside visual or aural perception can be tolerated. • Most lossy compression techniques can be adjusted to different quality levels. • Example: DCT(JPEG), MPEG

  23. Compression Ratio • Compression ratio original data size ------------------------- : 1compressed data size

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