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tomo/utils/fourier_interpolate.m

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+% function fourier_interpolate(val,theta,numord)
+% This function uses a Fourier transform approximation to obtain the zero
+% and first coefficient of a periodic function (a sine wave fit) if only data
+% of half a period is available. Data within 0 and 180 degrees (inclusive)
+% is given. Completes and takes fft of data, theta is only used for some
+% checks, should be given in radians.
+%
+% a*sin(x*pi/180+b)+c
+% Output phase is in radians
+%
+% It is meant to work with equally spaced angles in the range of 180
+% degrees, including 180 degrees. It allows not exactly equally spaced but then
+% accuracy cannot be guaranteed.
+%
+% Optional parameter numord can be used in order to retrieve higher orders
+% of the fit
+
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  Except where otherwise noted, this work is licensed under a          |
+%|  Creative Commons Attribution-NonCommercial-ShareAlike 4.0            |
+%|  International (CC BY-NC-SA 4.0) license.                             |
+%|                                                                       |
+%|  Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch)    |
+%|                                                                       |
+%|       Author: CXS group, PSI                                          |
+%*-----------------------------------------------------------------------*
+% You may use this code with the following provisions:
+%
+% If the code is fully or partially redistributed, or rewritten in another
+%   computing language this notice should be included in the redistribution.
+%
+% If this code, or subfunctions or parts of it, is used for research in a 
+%   publication or if it is fully or partially rewritten for another 
+%   computing language the authors and institution should be acknowledged 
+%   in written form in the publication: “Data processing was carried out 
+%   using the “cSAXS matlab package” developed by the CXS group,
+%   Paul Scherrer Institut, Switzerland.” 
+%   Variations on the latter text can be incorporated upon discussion with 
+%   the CXS group if needed to more specifically reflect the use of the package 
+%   for the published work.
+%
+% A publication that focuses on describing features, or parameters, that
+%    are already existing in the code should be first discussed with the
+%    authors.
+%   
+% This code and subroutines are part of a continuous development, they 
+%    are provided “as they are” without guarantees or liability on part
+%    of PSI or the authors. It is the user responsibility to ensure its 
+%    proper use and the correctness of the results.
+
+
+function fit = fourier_interpolate(val,theta,numord,sym_flip)
+% sym_flip  For a function that is only measured from 0 to 180 then the
+%           data is flipped mirrored in order to complete the period of 
+%           the sinewave
+
+% theta = [0:45:180]*pi/180;
+% val = 5 + sin(theta+0.5);
+if nargin<3
+    numord = 1;
+end
+
+if ~exist('sym_flip')
+    sym_flip = true;
+end
+ 
+% if any(theta)>1.05*pi;
+%     error('This routine cannot account for angles larger than 180 at the moment')
+% end
+
+if ~all(size(theta)==size(val))
+    error(['theta and val dont have the same number of elements'])
+end
+val = val(:);
+theta = theta(:);
+clear auxval
+if sym_flip
+    auxval = [val(:);-fliplr(val(2:end-1))+val(1)+val(end)];
+else
+    auxval = val;
+end
+auxfft = fft(auxval)/numel(auxval);
+fit.a = abs(auxfft(2:1+numord)*2*1i);
+fit.b = angle(auxfft(2:1+numord)*2*1i);
+fit.c = auxfft(1);
+
+
+% thetafine = linspace(0,pi,100);
+% figure(1);
+% plot(theta,val,'.-')
+% hold on
+% plot(thetafine,fit.a*sin(thetafine+fit.b)+fit.c,'-r')
+% hold off
+% 
+% figure(2);
+% plot(auxval,'.-');