e178-04L5

# e178-04L5 - Sampling and Quantization Lecture #5 January...

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Sampling and Quantization Lecture #5 January 20, 2004

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Sampling and Quantization & Spatial Resolution (Sampling) ± Determines the smallest perceivable image detail. ± What is the best sampling rate? & Gray-level resolution (Quantization) ± Smallest discernible change in the gray level value. ± Is there an optimal quantizer?
Image sampling and quantization In 2-D f(x,y) (Continuous image) Sampler f s (m,n) Quantizer u(m,n) To Computer

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1-D 1− D x(t) Time domain X(u) Frequency T s(t) x s (t) = x(t) s(t) = Σ x(kt) δ (t-kT) s(t) 1/T 1/T X s (f)
2-D: Comb function y comb(x,y; x ,∆ y ) x x y Comb( , ; , ) ( , ) xy x y x m xy n y n m ∆∆ ≅− =−∞ δ

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Sampled Image f xy xy x y fm x n y x m x y n y xy x y uv s n m (,) (, ; , ) (, ) ( , ) (,; , ) ,; , ) = =− ←→ = =−∞ comb comb COMB comb( ∆∆ ∆ ∆ δ 11 1
Sampled Spectrum F uv Fuv uv xy u k x v l y Fu k x v l y s kl (, ) , , , , =∗ F H G I K J =− F H G I K J =−∞ COMB 1 1 ∆∆ δ

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Sampled Spectrum: Example
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## This note was uploaded on 12/28/2011 for the course ECE 178 taught by Professor Manjunath during the Fall '08 term at UCSB.

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e178-04L5 - Sampling and Quantization Lecture #5 January...

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