# 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.
Alex Perrakis on 22 Nov 2021
And how am i able to compute this frequency? As you can the only data i have is those two images.
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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