Wrapped smoothing

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CP
CP 2011-5-31
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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回答（4 个）

Teja Muppirala
Teja Muppirala 2011-6-1
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');
  1 个评论
CP
CP 2011-6-2
Hmm I'm a bit confused and maybe because I wasn't clear. The data itself doesn't go from 0 to 360. So if the X axis is from 0 to 360 there are Y values that correspond to that, and I want to smooth those Y values such that those corresponding to 0 and 360 smooth together.

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Walter Roberson
Walter Roberson 2011-5-31
If you rescale the values first, you could use the unwrap() function to get continuous values; un-rescale and then do your smoothing.
John D'Errico
John D'Errico 2011-5-31
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])
Walter Roberson
Walter Roberson 2011-6-2
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 个评论
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John D'Errico
John D'Errico 2011-6-2
This will not ensure periodicity, only approximately so.
Walter Roberson
Walter Roberson 2011-6-2
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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