Digital Representations

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Digital Representations

• Digital Video Special Effects
• Fall 2006

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Analog-to-Digital (A-D) Conversion

• Sampling
• Quantization
• Coding

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Sampling -- Analog to Discrete

• Analog signal to discrete-time signal
• x(t) --gt xn
• Sampling procedure
• f(t) is the sampling function
• Simple sampling
• xn x(tn), i.e., f(t)d(t)

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Reconstruction Discrete to Analog

• Can we reconstruct analog signal from its
  discrete time samples?
• xn --gt 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

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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

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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)

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Digital Audio Signals

• Frequency band of sound human hearing frequency
  range 20Hz-20 KHz.
• Sampling rate gt 40 KHz (Actual sampling rate of
  CD-Audio 44.1 KHz)
• Bit rate for CD quality audio signal (44.1 KHz,
  Quantization16 bits, 2 channels)T 44100 x 16
  x 2 (bits per second, or bps)
• CD quality stereo sound ? 10.6 MB / min

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Examples
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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

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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 regarding
  specific musical actions.
• Commands, instead of actual waveforms, are saved.
  
• One minute of MIDI 4KB storage.

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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

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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

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Computer Graphics

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

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Video Signal Requirements

• Aspect ratio TV ? 4/3 HDTV?16/9
• Luminance and chrominance
• Continuity of motion gt 15 frames/s
• TV 30 or 25 frames/s, movie 24 frames/s
• Flicker. Marginal at least 50 refresh cycles/s
• Movie 2x2448
• TV Half picture by line-interleaving
• Scanning rate at lease 25Hz, finish one frame in
  1/25s

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Color Representation in Video

• RGB, normalized RGB1 -- white color
• YUV signal
• Y0.30R0.59G0.11B (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
• Y0.30R0.59G0.11B (Luminance)
• I0.60R-0.28G-0.32B, Q0.21R-0.52G0.31B
• Example NTSC
• Avoid cross talk between luminance and colors
  S-Video video signals separate the luminance and
  chrominance information into two separate analog
  signals.

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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
• YC1C2 -- 422
• Subsampling and upsampling techniques

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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

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Video Quality

• VCR Quality -- SIF (MPEG1)
• NTSC 240x352 PAL 288x352 per frame
• Videoconferencing quality
• CIF (Common Interchange Format) -- H.261
• 288x352, subsampling 411(halving both
  direction)
• Q what is the raw bit rate of CIF video
  (30frames/s)?
• QCIF (Quarter CIF)
• 144x176, subsampling 411(halving both
  direction)
• Q what is the raw bit rate of QCIF video
  (30frames/s)
• Super-CIF
• 576x704, subsampling 411(halving both
  direction)

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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!

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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.

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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.

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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

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Compression Ratio

• Compression ratio original data size
  ------------------------- 1compressed
  data size