MATLAB CURVE FITTING TOOLBOX - RELEASE NOTES User's Guide download pdf (Page 207)

smooth

4-131

The first four elements of yy are given by

yy(1) = y(1)

yy(2) = (y(1)+y(2)+y(3))/3

yy(3) = (y(1)+y(2)+y(3)+y(4)+y(5))/5

yy(4) = (y(2)+y(3)+y(4)+y(5)+y(6))/5

Because of the way that the end points are treated, the result shown above

differs from the result returned by the

filter function described in “Difference

Equations and Filtering” in the MATLAB documentation.

In this example, generate random data between 0 and 15, create a sine wave

with noise, and add two outliers with the value 3.

rand('state',2);

x = 15*rand(150,1);

y = sin(x) + (rand(size(x))-0.5)*0.5;

y(ceil(length(x)*rand(2,1))) = 3;

Smooth the data using the loess and rloess methods with the span specified

as 10% of the data.

yy1 = smooth(x,y,0.1,'loess');

yy2 = smooth(x,y,0.1,'rloess');

Plot original data and the smoothed data.

[xx,ind] = sort(x);

subplot(2,1,1)

plot(xx,y(ind),'r.',xx,yy1(ind),'k-')

set(gca,'YLim',[-1.5 3.5])

legend('Original Data','Smoothed Data Using ''loess''',2)

subplot(2,1,2)

plot(xx,y(ind),'r.',xx,yy2(ind),'k-')

set(gca,'YLim',[-1.5 3.5])

legend('Original Data','Smoothed Data Using ''rloess''',2)

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MATLAB CURVE FITTING TOOLBOX - RELEASE NOTES User's Guide Page 207