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31. Basics of 1-D signal quantization v2 - 2011

# 31. Basics of 1-D signal quantization v2 - 2011 - EE 638...

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EE 638: Principles of Digital Color Imaging Systems Lecture 29: Basics of 1D Signal Quantization

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1-D Quantization Basics Review Input: Output: threshold Uniformly Quantizer
I. Characterize Distortion Use MSE (Mean Squared Error) Signal Independent. for a reasonable no. of quantization levels

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Alternate viewpoint: Model as a stochastic i.e. is a r.v. for any fixed point to the density function
II. Derive Optimal 1-D Quantizer Question: Given , find Take derivative to the sum. D is constant (except i=j), which drive derivative to 0.

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If we know threshold, set If we know output levels, set the threshold in the middle Expectation of x given that x is in interval of
Algorithms 1-D Quantization: Loyd-Max Algorithm Vector Quantization: Linde-Buzo-Gray(LGB) Algorithm Similarly: k-means method in data clustering, ( which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean.)

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Scalar Quantization Scalar Quantization (1 variable) 1. uniform quantization

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31. Basics of 1-D signal quantization v2 - 2011 - EE 638...

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