Data Aquisition and Capture

Contents

Introduction

We consider the main issues concerning the digital or computer Acquisition of real world data.

Theoretical issues.
Conversion of  continuous-time, continuous amplitude signals measured
in the physical world into discrete-time, discrete amplitude data (or numbers) in a computer.
(i)	Discrete time signal
(ii)	Amplitude quantisation
(iii)	Sampling rate

Analog interface.
(i)	Signal Conditioning.
(ii)	Analog signal scaling.
(iii)	Analog to digital converter.

Analog acquisition systems.
(i)	Analog interface cards.
(ii)	Data buffering
(iii)	Data logging memory requirements.
(iv)	Single and multi-channel interfaces

Simulate sampling a Continuous Time Signal

Generate a 'continuous' time signal. Sample this sgnal at discrete time intervals and plot both signal together to see the relationship between them.

Continuous time signal: Signal frequency < Nyquist

Generate continuous time sinusoid, frequency = 0.5 Hz

f=.5; % Signal frequency
tmax=4;
fsc=10000;tc=1/fsc; %tc is the 'continuous time' sampling interval
t=0:tc:tmax; % Continuous time vector
x=cos(2*pi*f*t);
plot(t,x)
title('Continuous time signal , f = 0.5','fontsize', 15)

Sampled Signal

Sample the signal at 20 Hz

fs=20;
T=1/fs;
t_discrete=0:T:tmax;
xd=cos(2*pi*f*t_discrete);
hold on
stem(t_discrete,xd,'r','markerfacecolor','r')
title('Sampled Signal,   fs=20 ;    f signal = 0.5','fontsize', 15)

Zoom in

for i=0:100
    xlim([0 .5+3.5*(100-i)/100]);
    drawnow
end
hold off

Continuous time signal: Signal frequency> Nyquist

Aliased Signal:

The frequency of the continuous time signal is 19.5 Hz (remember the nyquist frequency is 10 Hz)

f=19.5; % Signal frequency
tmax=4;
fsc=10000;tc=1/fsc; %tc is the 'continuous time' sampling interval
t=0:tc:tmax; % Continuous time vector
x=cos(2*pi*f*t);
plot(t,x)
title('Continuous time signal , f = 19.5','fontsize', 15)

Sampled Signal

Sample the signal at 20 Hz

fs=20;
T=1/fs;
t_discrete=0:T:tmax;
xd=cos(2*pi*f*t_discrete);
hold on
stem(t_discrete,xd,'r','markerfacecolor','r')
title('Sampled Signal,   fs=20 ;    f signal = 19.5','fontsize', 15)

Zoom in

for i=0:100
    xlim([0 .5+3.5*(100-i)/100]);
    drawnow
end
hold off

Quantised Sampled Sinusoid

Q=0.1;   % Quantisation level
f=.082; % Signal frequency
tmax=20;
fsc=10000;tc=1/fsc; %tc is the 'continuous time' sampling interval
t=0:tc:tmax; % Continuous time vector
x=cos(2*pi*f*t);
plot(t,x);
% Sampled Signal
fs=1;
T=1/fs;
t_discrete=0:T:tmax;
xd=cos(2*pi*f*t_discrete);
set(gca,'xgrid','on','xtick',0:T:tmax,'ygrid','on','ytick',-1:Q:1)
hold on
plot(t_discrete,xd,'o','markerfacecolor','b')
title(['Sampled Signal,   f_s=' num2str(fs) ';    f_signal = ' num2str(f) ],'fontsize', 15)

Quantised Signal

xdq=floor(xd/Q)*Q;
stem(t_discrete,xdq,'sr','markerfacecolor','r')

Zoom in

axis([10 15 .3 1])
hold off

Quantisation Error

subplot(2,1,1)
xd=cos(2*pi*f*t_discrete);
set(gca,'xgrid','on','xtick',0:tmax,'ygrid','on','ytick',-1:1/10:1)
hold on
plot(t_discrete,xd,'o','markerfacecolor','b')
title(['Sampled Signal,   f_s=' num2str(fs) ';    f_signal = ' num2str(f) ],'fontsize', 15)
xdq=floor(xd*10)/10;
stem(t_discrete,xdq,'sr','markerfacecolor','r')

subplot(2,1,2)
e=xd-xdq;
stem(t_discrete,e);grid on
title('Quantisation Error')

Published with MATLAB® 7.1