Question

An analog to digital converter is to be designed for a digital communication system. In this converter, the output of the sampler varies between +3V and -3V.

a. Design a uniform quantizer with minimum peak signal power to average quantization noise power ratio equal to 28 dB. Draw a complete diagram of the quantizer clearly showing quantile interval and quantization levels. Show each design step in detail. Accuracy up to 4 decimal places is required.

b. Using the quantizer designed in part (a), quantize the following 10 values from sampler output. Draw a table that lists the quantized values vs. original values.

Sampler output values: [0.13, 1.72, 2.61, 0.63, 2.12, 1.1, 2.96, 0.5, 0.69, 2.71] volts

c. The quantizer designed in part (a) is to be used in the European landline telephone system but uniform quantization is usually not preferred for telephony applications and hence certain modifications are required. Modify the quantizer of part (a) so that it can be utilized for the above mentioned telephone system. Show the complete details of modification.

d. Using the modified quantizer obtained in part (c), quantize the sampler output values of part (b) and tabulate the results.

e. Compare the quantized values of part (b) and part (d) and comment if the modification done is working correctly.

Answer 1

Given that voltage is from 31 to tv and signal to nolse ratio 18 28 dB. we know that signal to nolse ratio (SNR) is given by- SNR= 1-766n st 176+60= 28 na 4.373 mes bits we know that step size (A) is given Az mare V min 2n so A= 3-6-32 25 TA= 0.1875 volt so Number of levels are given by in na No. of bits. so = 32 levels

so levels and quantizred value whee 0 -34vcm2.8175 Qu= -2.96875 - 2-819s <V - 263 ov-2.72375 6 -2.634V-2-uurs cer=-2.536251 32 2.8135 cvc 3 ceva 2.96875 2 block diagram of quantizer is- s-bit V -> eo 2 Quantizer

Table Is Sample value Quantized value 1-10625 2.96 2- 98125 0-5 0.13 0.5u375 016875 1-6 6 8 75 1-72 2-GI 0.69 2-71 2.60625 0-73125 2.79 375 0.54 375 2.64375 0-63 2-12