Shift in inverse Fourier Transform

Question

I have written a little script (MATLAB) using fast Fourier transform in order to filter messy time series.

Given a signal S(t) my function filter the n biggest amplitude components from the FFT transformation of S(t) and return's the filtered signal by inverse FFT.

The problem is that when I use a test signal the filtered signal is somehow shifted by approx. -1 in amplitude. I have tried to change the windowing but it doesn't appear to help (but the shift is moved toward +1).

Here is a sample code of my script:

% test Signal

t=0:0.1:1000;
f1=1/50; f2=1/300; f3=1/20;
Signal=100*sin(f1*2*pi*t)6x1+8*sin(f2*2*pi*t)+x3+x4+65*sin(f3*2*pi*t);

[FiltredSignal]=Filter(data,5,0); % call Filter function

figure
plot(t,real(a)*2,t,data) 

figure
plot(t,real(a)*2-data) % ???? shift of -1 in ifft ????


function [FiltredSignal]=Filter(Signal,n)   
% n= nbr of "most significative spectra components"

timelen=length(Signal);

FT=fft(Signal); % fast fourrier transform

FTcopy=FT/timelen; % Copy for spectral analysis
FTcopy(floor(timelen/2+1):end)=[]; % cut at nyquist point
FTcopy(1,1)=0; 


% sort FT2 in descending amplitude order
sortedFT=sort(abs(FTcopy),'descend');

% spectral selection --> n biggest amplitudes
FiltredFT=zeros(1,timelen); 
for i=1:n
  freq=find(abs(FTcopy)==sortedFT(i));      
  FiltredFT(freq)=FT(1,freq);
  %FiltredFT(freq-1)=FT(1,freq-1); % windowing
  %FiltredFT(freq+1)=FT(1,freq+1); % windowing
end

FiltredData=ifft(FiltredFT); % return filtred signal time serie

% END

Could someone explain what is happening?

I surely miss some theoretical facts of FFT (I am self learning so everything is not that clear).

Answer 1

Here is a revised version of the function above that is working, thanks to Paul R remarks.

function [FiltredSignal]=Filter(Signal,n)   
"% n= nbr of spectral components to keep "

timelen=length(Signal);

FT=fft(Signal); "% fast fourrier transform"

FTcopy=FT/timelen; "% Copy for spectral analysis"
FTcopy(floor(timelen/2+1):end)=[]; "% cut at nyquist point"


"% sort FT2 in descending amplitude order"
sortedFT=sort(abs(FTcopy),'descend');

"% spectral selection --> n biggest amplitudes"

FiltredFT=zeros(1,timelen); 

for i=1:n
  freq=find(abs(FTcopy)==sortedFT(i));      
  FiltredFT(freq)=FT(1,freq);
end

"% return filtred signal time serie with complex conjugate reconstruction"
FiltredData=ifft(FiltredFT,'symmetric');