%test?script?fgg_1D_experiment.m?for?the?1D?NFFT?based?on?Fast?Gaussian
%Gridding.
%
%NOTE:?In?order?for?this?FGG_1D?to?work?the?C?
%file?“FGG_Convolution1D.c“?must?be?compiled?into?a?Matlab?executable
%（cmex）?with?the?following?command:?mex?FGG_Convolution1D.c
%
%Code?by?（send?correspondence?to）:
%Matthew?Ferrara?Research?Mathematician
%AFRL?Sensors?Directorate?Innovative?Algorithms?Branch?（AFRL/RYAT）
%Matthew.Ferrara@wpafb.af.mil


clear?all;
close?all;
%clc
%path（path?‘./nfftde‘）;%NFFT?mex?files?from?Potts?et?al.

%?make?an?“image“
%Note?for?even?lengths?the?Nfft?routine?defines?the?image-space?origin
%?at?pixel?location?[Nx/2?+?1?Ny/2?+?1].
%?Convention:??x?counts?down?rows?y?counts?L?to?R?columns.
N=16;%even?length?assumed?below...tedious?to?generalize...
z?=?zeros（N1）;%
%Make?a?step?function:
z（8:12）=?1;
%imagesc（z）
img=double（z）;
%?Now?let‘s?compute?a?matlab?DFT?in?d?dimensions?using?the?“nfft“?command.
%?Note?use?fftshifts?to?match?indexing?convention?as?used?above?in?Pott‘s
%?nfft.
data=fftshift（ifftn（ifftshift（img）））;
DFTout?=?fftshift（fftn（ifftshift（data）））;
data=data（:）;

%?We?need?knots?on?[-1/2?1-1/Nx]x[-1/2?1-1/Ny]?as?fundamental?period.
%?make?square?grid?of?knots?for?exact?comparison?to?fft
tmpx?=?linspace（-1/21/2?-1/N（1）?N（1））;%?tmpx（end）=[];

%this?creates?N+1?points?then?discards?point?at?+0.5.
%store?my?K?knots?as?a?d-by-K?matrix?（d=2?dimension?here）
%...following?four?lines?could?be?cleverly?vectorized?avoiding?loop.


knots=[tmpx（:）];
Nx=[N];
%set?the?desired?number?of?digits?of?accuracy?desired?from?the?NUFFT
%routine:
Desired_accuracy?=?6;%6=single?precision?12=double?precision.
tic
MattOut_Gauss=FGG_1d_type1（data（:）knots[Nx]Desired_accuracy）;
plot（abs（MattOut_Gauss））
title（‘（Type-I?Fast?Gaussian?Gridding）?NFFT?output‘）
disp（[‘NUFFT?evaluated?in?‘num2str（toc）‘?seconds‘]）

MattOut_T2=iFGG_1d_type2（MattOut_GaussknotsDesired_accuracy）;
MattOut_Gauss2=FGG_1d_type1（MattOut_T2（:）knots[Nx]Desired_accuracy）;

figure
plot（1:Nabs（MattOut_Gauss2）‘-‘1:Nabs（img（:））‘.‘）
title（‘（Fast?Gaussian?Gridding）?NFFT-I?output?vs?DFT‘）


figure
plot（abs（DFTout（:）-MattOut_Gauss2（:）））
title（‘Error?between?DFT?and?NFFT‘）
Mean_Error=mean（abs（MattOut_Gauss（:）-DFTout（:）））

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2015-02-07?10:19??NUFFT_code\
?????文件????????9561??2009-10-14?05:02??NUFFT_code\FGG_1d_type1.m
?????文件???????10674??2009-10-14?05:02??NUFFT_code\FGG_2d_type1.m
?????文件???????12269??2009-10-14?05:03??NUFFT_code\FGG_3d_type1.m
?????文件????????6805??2009-10-14?05:06??NUFFT_code\FGG_Convolution1D.c
?????文件????????6680??2009-10-14?05:07??NUFFT_code\FGG_Convolution1D_type2.c
?????文件????????8175??2009-10-14?05:07??NUFFT_code\FGG_Convolution2D.c
?????文件????????8283??2009-10-14?05:07??NUFFT_code\FGG_Convolution2D_type2.c
?????文件????????9763??2009-10-14?05:07??NUFFT_code\FGG_Convolution3D.c
?????文件????????9819??2009-10-14?05:07??NUFFT_code\FGG_Convolution3D_type2.c
?????文件????????2301??2009-10-14?05:01??NUFFT_code\fgg_1D_experiment.m
?????文件????????2575??2009-10-14?05:01??NUFFT_code\fgg_2D_experiment.m
?????文件????????2679??2009-10-14?05:01??NUFFT_code\fgg_3D_experiment.m
?????文件????????6538??2009-10-14?05:05??NUFFT_code\iFGG_1d_type2.m
?????文件????????8322??2009-10-14?05:05??NUFFT_code\iFGG_2d_type2.m
?????文件????????7974??2009-10-14?05:05??NUFFT_code\iFGG_3d_type2.m