Scalar and Vector Quantization

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Quantized Bitrate with FLC If the number of quantizer output is M, then the bitrate of the quantizer output is R = ⎡log 2 M⎤ Eample: M = 8 → R = 3 Quantizer design problem: Given an input pdf f X (x) <strong>and</strong> the number of levels M in the quantizer, find the decision boundaries {b i } <strong>and</strong> the reconstruction levels {y i } so as to minimize the mean squared quantization error 8/55
Quantized Bitrate with VLC For VLC representation of quantization intervals, the bitrate depends on decision boundary selection Example: eight-level quantizer: R = = M ∑ i= 1 M ∑ i= 1 l P( y ) l i i ⎡ ⎢⎣ ∫ b b i i−1 i f X ( x) dx⎤ ⎥⎦ 9/55
Page 1 and 2: Scalar and Vector Quantization Nati
Page 3 and 4: The Quantization Problem Encoder m
Page 5 and 6: Quantization Function A quantizer
Page 7: Quantization Error If the quantiza
Page 11 and 12: Uniform Quantizer All intervals ar
Page 13 and 14: Uniform Quantization of Uniform Sou
Page 15 and 16: The SNR of Quantization For n-bit
Page 17 and 18: Quantization of Non-uniform Sources
Page 19 and 20: Solving for Optimum Step Sizes Giv
Page 21 and 22: Variance Mismatch Effects (1/2) Ef
Page 23 and 24: Distribution Mismatch Effects Give
Page 25 and 26: Forward Adaptive Quantization (FAQ)
Page 27 and 28: Speech Quantization Example (2/2)
Page 29 and 30: Backward Adaptive Quantization (BAQ
Page 31 and 32: Output Levels of 3-bit Jayant Quant
Page 33 and 34: Picking Jayant Multipliers We must
Page 35 and 36: Jayant Quantizer Performance To av
Page 37 and 38: pdf-optimized Quantization Given f
Page 39 and 40: Lloyd-Max Algorithm (2/3) Begin wi
Page 41 and 42: Example: pdf-Optimized Quantizers
Page 43 and 44: Companded Quantization (CQ) In com
Page 45 and 46: Example: CQ (2/2) The expandar fun
Page 47 and 48: Entropy Coding of Quantizer Outputs
Page 49 and 50: Why Vector Quantization (1/2)? Cor
Page 51 and 52: Vector Quantization Rule Vector qu
Page 53 and 54: The Linde-Buzo-Gray Algorithm 1. St
Page 55: Impact of Training Set The trainin

Scalar and Vector Quantization

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