Image Sampling

• A function f(x,y) is called bandlimited if its Fourier Transform F(u,v) is zero outside a bounded region in the spatial frequency plane.
  
  then u₀, v₀ are the bandwidth of the image (in the x, y direction respectively)

• Sampling theorem: If sampling frequencies are:
  
  then F(u,v) can be recovered by an ideal Low Pass Filter:
  

• The frequency 2u₀, 2v₀ are called Nyquist rate.

• If the image is sampled at a rage < Nyquist rate, aliasing will occur. Aliasing error can be avoided by low-pass filtering the image first.

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Image Quantization

• in most application, use uniform quantization.

• 
  Other quantizer:

• e.g. Compander Ä to have different quantization at different amplitude level.