lecture9

# lecture9 - EE455/591 S ourceC oding and Huffm C an oding Re...

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EE455/591 EE455/591 Source Coding and Huffman Coding Source Coding and Huffman Coding Reading: Section 6.3.1. Part of 6.1 (pages 267-271) Reading: Section 6.3.1. Part of 6.1 (pages 267-271) Review: Nyquist Sampling Theorem Review: Nyquist Sampling Theorem Topics: Topics: 1. What is Information? 1. What is Information? 2. Variable Length Coding 2. Variable Length Coding 3. Huffman Coding Algorithm 3. Huffman Coding Algorithm 4. Example of n-extension of Huffman tree 4. Example of n-extension of Huffman tree

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Review of Nyquist Sampling Theorem At transmitter, multiply x(t) with impulse train: At receiver, filter signal with low pass filter: t - - = n nT t T nT t T nT x t x ) ( )) ( sin( ) ( ) ( π W max -W max W max Time domain Frequency domain t 2W samples per second T -T 0 0 1/T -1/T f X(f) f t t W max X(f) f X Send sample values x(nT) Low Pass Filter [-1/(2T), 1/(2T)] X(t) X(t) if W max <1/(2T)
1. What is Information? Example: M={Phoenix rains today, Phoenix does not rain today} The message can be represented by 1 bit (0 or 1) Since Phoenix rains for less than 30 days of the year, there is not much information in this statement ( < 1 bit) Self information of a message: If message m in M occurs with probability p m , then I m = -log 2 p m bits Source information (Entropy) = average self information For example, the entropy of “being rainy” in Phoenix is only 0.425 bits per

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lecture9 - EE455/591 S ourceC oding and Huffm C an oding Re...

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