Signal Sampling and Quantization - Digital Signal Processing: Fundamentals and Applications - page 44

EXAMPLE 2.13
Given a sinusoidal waveform with a frequency of 100 Hz,
xðtÞ¼4:5$sinð2p 100tÞ

sampled at 8,000 Hz,
a. write a MATLAB program to quantize xðtÞ using 4 bits to obtain and plot the quantized signal x q , assuming the
signal range is between 5 and 5 volts;
b. calculate the SNR due to quantization.
Solution:
a. Program 2.1. MATLAB program for Example 2.13.
%Example 2.13
clear all; close all
disp( ' Generate 0.02-second sine wave of 100 Hz and Vp ¼ 5 ' );
fs ¼ 8000;

% Sampling rate

T ¼ 1/fs; % Sampling interval

t ¼ 0:T:0.02; % Duration of 0.02 second

sig ¼ 4.5*sin(2*pi*100*t); % Generate sinusoids

bits ¼ input( ' input number of bits ¼ > ' );
lg ¼ length(sig); % Length of signal vector sig

for x 1:lg

[Index(x) pq]

¼

¼ biquant(bits, -5,5, sig(x)); % Output quantized index

5

4

3

2

1

0

-1

-2

-3

-4

-5

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Time (s ec . )

FIGURE 2.33
Comparison of the quantized signal and the original signal.