Wrapped smoothing
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I have some data that lies on a wrapped dimension (e.g. 0 to 360) and I want to smooth it using something like lowess etc. However, I want the smoothing to wrap so that points near 360 smooth with points near 0. Any quick and easy way to get this done?
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Answers (4)
Teja Muppirala
on 1 Jun 2011
Step 1. Rescale from (0,360) to (-pi,+pi)
Step 2. Unwrap the data using UNWRAP
Step 3. Smooth it
Step 4. Rescale from (-pi,+pi) back to (0,360)
Step 5. Rewrap the data using MOD
(Steps 4 and 5 are swappable).
%%Step 0 - Make some phony data
ph = 360*interpft(randn(1,5),1000);
ph = ph+10*randn(size(ph));
ph = mod(ph,360);
figure(1);
plot(ph);
%%Step 1
ph = ph*pi/180-pi;
figure(2);
plot(ph);
%%Step 2
ph = unwrap(ph);
figure(3);
plot(ph);
%%Step 3
ph = smooth(ph,25);
hold on;
plot(ph,'r');
%%Step 4
ph = 180/pi*ph+180;
%%Step 5
ph = mod(ph,360);
figure(1);
hold on;
plot(ph,'r');
Walter Roberson
on 31 May 2011
If you rescale the values first, you could use the unwrap() function to get continuous values; un-rescale and then do your smoothing.
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John D'Errico
on 31 May 2011
You can use my SLM tools, with knots defined over 0-360 degrees, but specify periodic end conditions.
For example, this fit works nicely:
X = rand(100,1)*360;
Y = sind(X) + randn(size(X))/5;
slm = slmengine(X,Y,'knots',linspace(0,360,7), ...
'endconditions','periodic','plot','on', ...
'concavedown',[0,150],'concaveup',[210,360])
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Walter Roberson
on 2 Jun 2011
The easiest way might be to replicate the initial data at the end, using as many duplicate points as your smoothing window is wide. Smoothing done, clip off those extra points.
You would have to figure out what to do about the point for 360 being at the same place as the point for 0; possibly drop the last point if it is at 360 or higher.
3 Comments
Walter Roberson
on 2 Jun 2011
If your measured value for 0 is different from the measured value for 360 to beyond the noise level, getting periodicity would require fudging the numbers.
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