Biosignal Processing - Introduction to Biomedical Engineering - page 726

the procedure may include using overlapping segments if a larger value for is needed and

the number of available data points is not sufficient and/or multiplying each section by a
window that forces continuity at the end points of the segments.

L

EXAMPLE PROBLEM 11.27
Consider the sinusoid signal

x ð k Þ¼ sin ðp= 4 k Þþ n ð k Þ

that is corrupted by random noise, ). Using MATLAB, show that averaging the signal removes

the noise component and reveals the deterministic component. Show results for 1, 10, and 100
averages.

n ( k

Solution
k

¼

1:64; %Discrete Time Axis
for i

¼

1:100 %Generating 100 signal Trials
x(i,:)

¼ þ

sin(pi/4*k) randn(1,64); %i-th trial

end
X1

¼

x(1,:); %1 Averages

¼

X10 mean(x(1:10,:)); %10 Averages

¼

X100 mean(x); %100 Averages

subplot(311) %Plotting Results, 1 Average
plot(k,X1,'k')
axis([1 64 -3 3])
title('1 Average')
ylabel('Amplitude')

subplot(312) %Plotting Results, 10 Averages
plot(k,X10,'k')
axis([1 64 -3 3])
title('10 Averages')
ylabel('Amplitude')

subplot(313) %Plotting Results, 100 Averages
plot(k,X100,'k')
axis([1 64 -3 3])
title('100 Averages')
xlabel('Discrete Time')
ylabel('Amplitude')

The results are shown in Figure 11.28.