Matlab傅立叶反卷积

编程问答 2022-08-15

问题描述

我试图对测得的光谱（Sm）与纯光谱（S0）进行反卷积，以获得切趾和乐器线形。以下是文件：Sm和S0

但是，我发现Sm和S0的ifft结果相似。它应该给我高斯线形，但是我得到了三角形。我的错误是什么以及如何解决？ 预先谢谢你。

close all
clear all 
clc
sm=load('n2o_gaussian.txt');                     %loading spectrum with gaussian ILS
s0=load('n2o_noapodization.txt');                %loading pure spectrum

v=s0(:,1);                                       %wavenumber of pure spectrum
s0_y=s0(:,2);                                    %y component of S0
L=length(v);                                     %length of data
n=2^(nextpow2(L)*2);                             %number of the next power of two data for FFT

vm=sm(:,1);                                      %wavenumber of measured spectrum
v0=2217.241;                                     %v0 is peak location
vv0=v*ones(1,length(v0))-ones(length(v),1)*v0;   %vv0 is wavenumber difference

sm_interpl=interp1( vm,sm,v,'spline',0);      %fit the measured spectrum to match the grid 
                                                 %pure spectrum                            
sm_interpl_y=sm_interpl(:,2);                    %y component of Sm

%y-deconvolution of Sm with S0
s0_y_ift=ifft(s0_y,n,'symmetric');               %inverse FFT of pure spectrum,the symmetric option 
                                                 enforces imaginary part should be zero in DFT
s0_y_ift=fftshift(s0_y_ift);
sm_interpl_ift=ifft(sm_interpl_y,'symmetric'); %inverse FFT of measured spectrum,without 
                                                 symmetric,half of amplitude will lost
sm_interpl_ift=fftshift(sm_interpl_ift);


apo_y=(sm_interpl_ift)./(s0_y_ift);              %get the apodization function from division of sm 
                                                 and s0
ILS_y=fft(apo_y,n);                              %get the ILS
ILS_y2=fftshift(ILS_y);

     
%normalize the area of ILS
area=trapz(f,ILS_y2);
ILS_y2_normalized=ILS_y2./area;

%showing spectra and spline result
figure (1)
plot (sm(:,1),sm(:,2),'o');
hold on;
plot (sm_interpl(:,sm_interpl(:,2));
hold on
plot (s0(:,s0(:,2));
legend('Measured spectrum','fitted spectrum','pure spectrum')
hold on;

%showing interferogram results
figure (2)
plot(real(sm_interpl_ift))
hold on
plot(real(s0_y_ift))
legend('interferogram of Sm','interferogram of S0')
hold on

%showing apodization function
figure (3)
plot(real(apo_y))
legend('apodization function')
hold on

%showing retrieved ILS
figure (4);
plot(f,real(ILS_y2_normalized));
xlim([-0.0001 0.0001]); 
legend('ILS');
hold on;

解决方法

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