$6.[25$pts$]$

a$.$ Determine and illustrate the partition levels and reconstruction levels of a uniform

quantizer in the range of $(-2,2)$ with $8$ levels.

b$.$ Determine and illustrate the partition levels and reconstruction levels of a $-$law

quantizer in the range of $(-2,2)$ with $8$ levels, $=15.$

c$.$ For the sequence $\{0\mathrm{.}3,-0\mathrm{.}8,-1\mathrm{.}9,-1\mathrm{.}3,1\mathrm{.}15,-0\mathrm{.}2,...\},$ determine the quantized sequence

using the uniform and $-$law quantizers. Determine the mean square quantization error

and SNR for both quantizers. For this sequence, which method $($uniform vs$.$ $-$law$)$

gives a more accurate result? Hint: Mean square quantization error is given by

$$

n

q x n x n

N

$2(()())2$

$1$

; variance of the input sequence is given by

$$

n

x x n E x

N

$2(()[]))2$