pcshw7_soln

# pcshw7_soln - THE STATE UNIVERSITY OF NEW JERSEY RUTGERS...

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THE STATE UNIVERSITY OF NEW JERSEY RUTGERS College of Engineering Department of Electrical and Computer Engineering 332:322 Principles of Communications Systems Spring 2004 Problem Set 7 Haykin section 3.6 Web notes on convexity Web notes on quantization 1. Quantization: Show that a nonuniform quantizer with sufficiently small bin sizes i , has mean-square quantization error of approximately 1 12 i 2 i p i , where p i is the probability that the input signal amplitude lies within the i th interval. HINT: You may assume that for i sufficiently small, you have an approximately uniform distribution given that x lies in the i th bin. SOLUTION: First we invoke Lloyd-Max. Since we assume the conditional distribution in any bin is approximately uniform, we must have the associated level q i as the midpoint of the bin. If the bin starts at x i 1 , it must end at x i x i 1 i . Then we must have q i x i 1 i 2 (or q i x i i 2 ). Let’s talk only in terms of the q i . Then we know that the i

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• Spring '08
• Rose
• Probability theory, bin, 1 j, 4 bit, College of Engineering Department of Electrical and Computer Engineering, 1 30 16 j

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pcshw7_soln - THE STATE UNIVERSITY OF NEW JERSEY RUTGERS...

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