pcshw7 - x lies in the i th bin. 2. Quantization Example:...

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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 sufFciently small bin sizes Δ i , has mean-square quantization error of approximately 1 12 i Δ 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 Δ i sufFciently small, you have an approximately uniform distribution given that
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Unformatted text preview: x lies in the i th bin. 2. Quantization Example: (a) A random waveform x ( t ) has amplitude uniformly distributed over [-1 , 1] . Please provide an optimal 4 bit quantizer for this signal. Show your choice satisFes the Lloyd-Max optimality conditions. (b) Let x (0) be a quantized sample of the signal level x ( t ) . What is E [ x (0)-x ( t )] ? What is E [( x (0)-x ( t )) 2 ] ? What is the probability distribution on the random variable e (0) = x (0)-x ( t ) ? You must justify your results. 1...
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