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hw4_sol - ECE 638 Principles of Digital Color Imaging...

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ECE 638: Principles of Digital Color Imaging Systems Homework No.4 Name: Qiqi Wang Problem 1. Solution: Because the density function is symmetric to x=0 and it is a 2-level quantizer, we could easy figure out the threshold should be set at 0, so we need to find out the output level for these 2 level quantizer. For minimizing the mean-squared error, the output level should satisfy the following condition. 1 1 1 ( ) { | } ( ) x x x x x x x p x dx y E x x x x p x dx + + + = = < A A A A A A A So we could find out 1 0 3 1 1 1 0 3 1 5 ( ) 8 4 5 8 1.25 1 4 1 1 2 8 4 x x dx x dx y dx dx + = = = − = − + Using the same approach, 3 1 1 0 2 3 1 1 0 5 ( ) 8 4 5 8 1.25 1 4 1 1 2 8 4 x x dx x dx y dx dx + = = = = + So the 2-level quantizer should be 1.25, when x<0 ( ) { 1.25, when x 0 Q x =
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