# Sampling and Reconstruction The sampling and reconstruction process

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• ## The sampling and reconstruction process

• Real world: continuous
• Digital world: discrete
• ## Basic signal processing

• Fourier transforms
• The convolution theorem
• The sampling theorem
• ## Aliasing and antialiasing

• Uniform supersampling
• Nonuniform supersampling

## Camera Simulation

• Sensor response
• Lens
• Shutter

• ## Examples:

• Retina: photoreceptors
• CCD array

• ## Examples:

• DACs: sample and hold
• Cathode ray tube: phosphor spot and grid

• ## Artifacts due to sampling - Aliasing

• Jaggies
• Moire
• Flickering small objects
• Sparkling highlights
• Temporal strobing

• ## This result if known as the Sampling Theorem and is due to Claude Shannon who first discovered it in 1949

• A signal can be reconstructed from its samples
• without loss of information, if the original
• signal has no frequencies above 1/2 the
• Sampling frequency

• ## Unfortunately,

• The sinc has infinite extent and we must use simpler filters with finite extents. Physical processes in particular do not reconstruct with sincs
• The sinc may introduce ringing which are perceptually objectionable

• ## Analytically prefilter the signal

• Solvable for points, lines and polygons
• Not solvable in general
• e.g. procedurally defined images

• ## Uniform sampling

• The spectrum of uniformly spaced samples is also a set of uniformly spaced spikes
• Multiplying the signal by the sampling pattern corresponds to placing a copy of the spectrum at each spike (in freq. space)
• Aliases are coherent, and very noticable
• ## Non-uniform sampling

• Samples at non-uniform locations have a different spectrum; a single spike plus noise
• Sampling a signal in this way converts aliases into broadband noise
• Noise is incoherent, and much less objectionable

## Poisson Disk Sampling

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