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lecture10 - E E455/ 591 D i gi ti zi ng Anal og Si gnal s...

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EE455/ 591 EE455/ 591 Digitizing Analog Signals - Digitizing Analog Signals - Quantization Quantization Reading: Section 6.5.1 Reading: Section 6.5.1 Review: Huffman Coding for n-Extension Review: Huffman Coding for n-Extension Topics: Topics: 1. Sampling and Quantization of Speech 1. Sampling and Quantization of Speech 2. Scalar Quantization 2. Scalar Quantization 3. Computing SQNR for Uniform Quantizer 3. Computing SQNR for Uniform Quantizer
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Review: n-Extension of Huffman Coding M={a,b,c} with P a =1/ 8, P b =3/ 8, P c =4/ 8 and H(M)=1.405 bit Construction of Huffman tree using two letter words M={aa, ab, ac, ba, bb, bc, ca, cb, cc} Probability of 2-letter word equals product of probability of each letter, e.g. P cc = P c x P c = 16/ 64 Code: Prob.: Word: Branches: 11 16/ 64 cc 01 12/ 64 cb 101 12/ 64 bc 100 9/ 64 bb 0011 4/ 64 ca 0010 4/ 64 ac 0001 3/ 64 ba 00001 3/ 64 ab 00000 1/ 64 aa Expected codeword length =2.86 > 2x1.405 This is better than 1-extension {a, b, c} with 1.5 bit/ letter Question: Can we achieve H(M) bit/ letter? Answer : Yes for large n 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 Efficiency of n-extension: nH(M)+1 E[L] nH(M) 27/ 64 37/ 64 64/ 64 21/ 64 4/ 64 8/ 64 15/ 64 7/ 64
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1. Sampling and Quantization of Signals
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lecture10 - E E455/ 591 D i gi ti zi ng Anal og Si gnal s...

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