test_FFT.txt
function test_FFT(flag)
% Test GUI for playing with FFTs:
% Please do not pass any parameter when calling this program.
% Variables that should be kept in memory from call to call:
persistent lst width offset x k;
if(nargin > 0)
% Obtain user selected values:
func = get(lst,'Value')
w = str2double(get(width,'String'));
x0 = str2double(get(offset,'String'));
% Produce the correct function, according to user input:
switch func
case 1 % Gaussian
f = exp(-((x-x0)/w).^2);
case 2 % Top hat aperture
f = zeros(size(x));
f(find(abs(x-x0)<w/2)) = 1;
end
% Obtain the modulus of the Fourier transform
frMod = abs(ifftshift(fft(fftshift(f))));
% Obtain the phase of the Fourier transform
frPhase = angle(ifftshift(fft(fftshift(f))));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Plot the data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The function itself:
subplot(2,2,2);
plot(x,f); axis tight; ylim([0 1.2*max(f)]);
fwhm = FWHM(x,f);
title(sprintf('f(x) [FWHM=%.2f]',fwhm)); xlim([-10 10]); xlabel('x in nm');
% Modulus of the FFT
subplot(2,2,3);
plot(k,frMod); axis tight; ylim([0 1.2*max(frMod)]); xlim([-10 10])
fwhm = FWHM(k,frMod);
title(sprintf('|FFT(f)| [FWHM=%.2f]',fwhm)); xlabel('k in 1/nm');
% Phase of the FFT
subplot(2,2,4);
plot(k,frPhase); axis tight; ylim([-1.1*pi 1.1*pi]); xlim([-10 10])
title('arg[FFT(f)]'); xlabel('k in 1/nm');
else
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Setup the window and graphical user interface controls,
% if this function has been called with no input.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Define real- and reciprocal space arrays
dx = 0.001;
x = -20:dx:20-dx;
N = length(x);
dk = 1/(max(x)-min(x));
k = dk*[-N/2:N/2-1];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Do the GUI setup
figure('Color',[0.8 0.8 0.8],'Name','FFT test GUI')
funcs = {'Gaussian';'Top Hat Aperture'};
% Listbox with function names
lst = uicontrol('Units','normalized', ...
'Position',[.3, .8,.19,.07],...
'String',funcs,'Style','listbox','Callback','test_FFT(1)');
% Edit control for function widths
width = uicontrol('Units','normalized', ...
'Position',[.3, .7,.19,.03],...
'String','1','Style','edit','Callback','test_FFT(1)');
% Edit control for function shift
offset = uicontrol('Units','normalized', ...
'Position',[.3, .65,.19,.03],...
'String','0','Style','edit','Callback','test_FFT(1)');
% Text for function selection
lstT = uicontrol('Units','normalized', ...
'Position',[.1, .84,.19,.03],...
'String','function:','Style','text','Backgroundcolor',[0.8 0.8 0.8],...
'HorizontalAlignment','left');
% Text for Width selection
widthT = uicontrol('Units','normalized', ...
'Position',[.1, .7,.19,.03],...
'String','width:','Style','text','Backgroundcolor',[0.8 0.8 0.8],...
'HorizontalAlignment','left');
% Text for offset selection
offsetT = uicontrol('Units','normalized', ...
'Position',[.1, .65,.19,.03],...
'String','x0:','Style','text','Backgroundcolor',[0.8 0.8 0.8],...
'HorizontalAlignment','left');
% Call this program which is now initialized
test_FFT(1);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% A sinple function for determining the full width at half maximum
% Input:
% x1: the array of x-values
% f1: the array of function values
% Output:
% fwhm: FWHM of f in the scale given by x
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function fwhm = FWHM(x1,f1)
f1s = f1-0.5*max(f1);
ind = find(f1s(1:end-1).*f1s(2:end) <=0);
fwhm = x1(ind(2))-x1(ind(1));