# Find Periodicity of a plot to do Fourier Transformation

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Alex Perrakis on 22 Nov 2021
Commented: Star Strider on 22 Nov 2021
Hello Guys, i have following code, and which produces some plots, i would like to find the periodicity of the plot to do a Fourier. But it does not work, maybe one of you can tell me why?
newpicture=imsubtract(pic01,pic050);
%imshow(newpicture)
% level = graythresh(newpicture);
level = 0.1405;
newbinpic = imbinarize(newpicture,level);
%imshowpair(newpicture,newbinpic,'montage')
newbinpic2=bwpropfilt(newbinpic,'perimeter',1);
% imshowpair(newbinpic2,newpicture,'montage');
boundaries = bwboundaries(newbinpic2,'noholes');
% Plot raw (x,y) values
x = boundaries{1}(:,2);
y = boundaries{1}(:,1);
figure()
subplot(2,2,1)
plot(x,y, 'r-')
title('raw values')
axis equal tight
hold on
% Assuming (x,y) is a noisy circle, find center
cnt = [min(x)+range(x)/2, min(y)+range(y)/2];
xline(cnt(1))
yline(cnt(2))
% Shift to (0,0) and compute polar coordinates
[theta, rho] = cart2pol(x-cnt(1), y-cnt(2));
% Plot in polar coord
subplot(2,2,2)
polarplot(theta, rho)
title('Polar coord.')
% Define a reasonable threshold to isolate the spike in RHO values
% 90% of the median looks OK
subplot(2,2,3)
plot(rho)
threshold = median(rho)*.9;
yline(threshold, '-k', 'Threshold')
ylabel('rho'); xlabel('index')
title('rho values')
% Find start and end of peak
peakIdx = find(rho < threshold);
peakIdx(2:end-1) = [];
xline(peakIdx(1)) % plot start of peak
xline(peakIdx(2)) % plot end of peak
% Remove the peak
theta(peakIdx(1):peakIdx(2)) = []; % you can do the same with x
rho(peakIdx(1):peakIdx(2)) = []; % you can do the same with y
% Plot the circle without the interior object
subplot(2,2,4)
plot(theta,rho)
t=[1:1:1730]';
title('Inner removed')
[pks,locs] = findpeaks(rho(:,1)); % Peaks & Locations
mean_period = mean(diff(t(locs))); % Period
text(min(thetalim)+0.1*diff(thetalim), min(thetalim)+0.95*diff(thetalim), sprintf('Mean Period = %.2f time units', mean_period))
I attached the Pictures, but because it does not accept .tiff , i uploaded in png, just change it in the code.
Star Strider on 22 Nov 2021
For spatial data, the sampling interval would be the pixel interval in each dimension. Add spatial calibration (e.g. parsecs/pixel) if available and necessary. The rest follows directly.
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