1-Why digital control? 2- What is ADC ? Draw the electronic circuit. 3- Explain the effect of sampling time and the number of word length n on quantization error. 4- Calculate quantization error
1-Why digital control? 2- What is ADC ? Draw the electronic circuit. 3- Explain the effect of sampling time and the number of word length n on quantization error. 4- Calculate quantization error
Chapter25: Television, Telephone, And Low-voltage Signal Systems
Section25.3: Signal System
Problem 1R
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form the pic solve?
1-Why digital control?
2- What is ADC ? Draw the electronic circuit.
3- Explain the effect of sampling time and the number of word length n on quantization error.
4- Calculate quantization error
![Software Used: MATLAB
1-Enter the program in this page. This is a simple program to demonstrate the effect of
quantization on the accuracy of digital signals.
2-Adjust the number of bits, n, and observe the effect on the quantization error.
3-Draw the Sampled signal versus Quantized signal for sampling frequency fs=20 Hz with
(n=3, 8 &10) and repeated with fs=10 Hz.
% This program quantizes a signal to n bits.
% It demonstrates, in simple terms, the operation of a typical
ADC.
% This code assumes the signal is between -1 and +1.
clc
clear
close all
n=3;
Tsample
ts =
0/0/0/0/
= 0.05; %%%% 2)0.1,,,Tsample (11fs)
0:Tsample:2;
X = sin (2*pi*1*ts) ; % sampled digital signal
%x-sawtooth (2*pi*1*ts); %...you might wish to try a sawtooth
waveform
xn1 = x + 1; %Signal is shifted, now 0 to 2
xn2
=
of bits
xn3 = floor(xn2); %Signal is quantized, floor rounds number
down to integer
xn4=xn3/(2^(n-1)); %Signal is scaled back down, now 0 to 2
(quantized)
xn5=xn4-1; %Shift signal down (rounding) % Quantized signal
figure (1)
hold on;
stem(x, 'b'); %%%%% Sampled signal
hold on;
stem(xn5, 'r'); %%%%% quantized signal
legend('exact', 'quantized')
title(sprintf('Sampled signal versus Quantized signal'));
hold off
xerror = X xn5; % % quantization error.
figure (2)
stem(xerror,'g');
title(sprintf('Quantization Error'));
ylim ( [0 1])
-0.2
Sampled signal versus Quantized signal
8
8
M
-0.4
% Number of ADC bits; n=3, 8, 10
-0.6
xn1*2^(n-1); %Signal is scaled to ADC range, n = number
-0.8
-1
0
5
10
exact
quantized
Fig.4: Sampled signal versus Quantized signal
for n=3 & Ts=0.05
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
15
Quantization Error
20
25
30
35
40
Fig.5: Quantization Error
for n=3 & Ts=0.05](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef9570cd-2bc8-421b-b22f-944bce934f0b%2Fd0b6c139-9880-472b-ab6b-150c6bf80f55%2Fk2kkm6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Software Used: MATLAB
1-Enter the program in this page. This is a simple program to demonstrate the effect of
quantization on the accuracy of digital signals.
2-Adjust the number of bits, n, and observe the effect on the quantization error.
3-Draw the Sampled signal versus Quantized signal for sampling frequency fs=20 Hz with
(n=3, 8 &10) and repeated with fs=10 Hz.
% This program quantizes a signal to n bits.
% It demonstrates, in simple terms, the operation of a typical
ADC.
% This code assumes the signal is between -1 and +1.
clc
clear
close all
n=3;
Tsample
ts =
0/0/0/0/
= 0.05; %%%% 2)0.1,,,Tsample (11fs)
0:Tsample:2;
X = sin (2*pi*1*ts) ; % sampled digital signal
%x-sawtooth (2*pi*1*ts); %...you might wish to try a sawtooth
waveform
xn1 = x + 1; %Signal is shifted, now 0 to 2
xn2
=
of bits
xn3 = floor(xn2); %Signal is quantized, floor rounds number
down to integer
xn4=xn3/(2^(n-1)); %Signal is scaled back down, now 0 to 2
(quantized)
xn5=xn4-1; %Shift signal down (rounding) % Quantized signal
figure (1)
hold on;
stem(x, 'b'); %%%%% Sampled signal
hold on;
stem(xn5, 'r'); %%%%% quantized signal
legend('exact', 'quantized')
title(sprintf('Sampled signal versus Quantized signal'));
hold off
xerror = X xn5; % % quantization error.
figure (2)
stem(xerror,'g');
title(sprintf('Quantization Error'));
ylim ( [0 1])
-0.2
Sampled signal versus Quantized signal
8
8
M
-0.4
% Number of ADC bits; n=3, 8, 10
-0.6
xn1*2^(n-1); %Signal is scaled to ADC range, n = number
-0.8
-1
0
5
10
exact
quantized
Fig.4: Sampled signal versus Quantized signal
for n=3 & Ts=0.05
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
15
Quantization Error
20
25
30
35
40
Fig.5: Quantization Error
for n=3 & Ts=0.05
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