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HW3_solution - EE3414 Homework#3 Solution 1 Determine and...

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EE3414 Homework #3 Solution 1. Determine and illustrate the partition levels and reconstruction levels of a uniform quantizer in the range of (-1, 1) with 4 levels. Solution: The entire data range is -1+1=2 N=4, Q=2/4=0.5 The partition and reconstruction levels are illustrated below. 2. For the sequence {0.2,-0.3,-0.7, 0.8,}, a. Determine the quantized sequence using the uniform quantizer of Prob. 1. Also determine the mean square quantization error and SNR. b. Determine the binary stream corresponding to the quantized sequence. Solution: a. The quantized sequence is {0.25, -0.25, -0.75, 0.75}. The quantization error is To determine the SNR, we need to first determine the variance of the signal from the given samples. First we need to determine the mean value of the original samples: Mean=(0.2-0.3-0.7+0.8)/4=0.0 b. {10, 01, 00, 11} -1.0 -0.5 0 0.5 1.0 0.25 0.75 -0.75 -0.25 Reconstruction levels Partition levels 0025 . 0 ) 2 )^ 75 . 0 8 . 0 ( 2 )^ 75 . 0 7 . 0 ( 2 )^ 25 . 0 3 . 0 ( 2 )^ 25 . 0 2 . 0 (( 4 1 )) ( ˆ ) ( ( 1 2 2 = - + - + - + - = - = n q n x n x N σ ( 29 dB SNR mean n x N q x n x 97 . 20 0025 . 0
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