Determining the input from the output using IFFT

Question

Ganesh Prasad 2024-2-22

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2085218-determining-the-input-from-the-output-using-ifft

评论： William Rose 2024-3-3

采纳的回答： William Rose

images.png

在 MATLAB Online 中打开

Hello,

I have an output waveform y(t) after having passed through an S-matrix.I need to get the input signal x(t) and the method followed is:

1.Extract S21 from S-matrix and take IFFT of S21 to get the impulse response h(t)

2.convolve output waveform y(t) with 1/h(t) to get back input signal x(t).

The code is written below:

%Read the S parameter matrix and seperate the freq and s matrix data
sp=sparameters('C:\Users\PrasadNGanes\Desktop\snp_data\2Port.s2p');
freq=sp.Frequencies;
s=sp.Parameters;
%Seperate the S21 column from S-matrix and plot S21
S21=rfparam(sp,2,1);
rfwrite(S21,freq,'C:\Users\PrasadNGanes\Desktop\snp\newS21.s2p');
sp_inv=sparameters('C:\Users\PrasadNGanes\Desktop\snp\newS21.s2p');
figure;
rfplot(sp_inv);
title('S21 plot');
%Take IIFT of S21 to get impulse response h(t) and plot Impulse response
impulse_response=ifft(S21);
figure;
plot(impulse_response);
Fs = 2*max(freq);
Ts=1/Fs;
N=numel(impulse_response);
tvec=(0:(N-1))*Ts;
figure;
plot(tvec,impulse_response);
title('impulse response');
%convolve output y(t) with 1/h(t) to get back the input x(t)
inverse_impulse=1./impulse_response;
%read the output y(t)
data=xlsread('C:\Users\PrasadNGanes\Desktop\snp_data\probe_output.xlsx');
out_time=data(:,1);
output=data(:,2);
convolution_result=conv(output,inverse_impulse);
convolution_time=linspace(min(out_time)+min(tvec),max(out_time)+max(tvec),length(convolution_result));
figure;
plot(convolution_time,convolution_result);
title('input plot after convolution');
%Plot the real input and output
data=xlsread('C:\Users\PrasadNGanes\Desktop\probe.xlsx');
inp_time=data(:,1);
input=data(:,2);
figure;
plot(inp_time,input,'b');
hold on
plot(out_time,output,'r');
title('Actual output in red and input in blue');

However, I see that the input waveform got after running the code and the actual waveform do not match.I have attached the images for reference.

Can somebody help me what needs to be corrected to get the correct result.

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Ganesh Prasad 2024-2-26

编辑：Walter Roberson 2024-2-29

在 MATLAB Online 中打开

I have tried taking the conjugate of the S21 row vector, flipping it and adding to the original S21 and then taking IFFT.But the output is not as expected.

%Read the S parameter matrix and seperate the freq and s matrix data
sp=sparameters('C:\Users\PrasadNGanes\Desktop\snp_data\QVR_MX0100A_InfMode_SldrInFlat_Zin_2Port.s2p');
freq=sp.Frequencies;
s=sp.Parameters;
%Seperate the S21 column from S-matrix and plot S21
S21=rfparam(sp,2,1);
rfwrite(S21,freq,'C:\Users\PrasadNGanes\Desktop\snp\newS21.s2p');
sp_inv=sparameters('C:\Users\PrasadNGanes\Desktop\snp\newS21.s2p');
figure;
rfplot(sp_inv);
title('S21 plot');
fs=26999*10^6;
N=length(freq);
dt=1/fs;
t=(0:N-1)*dt;
S21_t=transpose(S21);
reconstructed_fft = [S21_t, conj(fliplr(S21_t(2:end-1)))];
%Take IIFT of S21 to get impulse response h(t) and plot Impulse response
impulse_response=ifft(reconstructed_fft);
figure;
plot(impulse_response);
title('impulse response');
%convolve output y(t) with 1/h(t) to get back the input x(t)
inverse_impulse=1./impulse_response;
%read the output y(t)
data=xlsread('C:\Users\PrasadNGanes\Desktop\snp_data\probe_output.xlsx');
out_time=data(:,1);
output=data(:,2);
convolution_result=conv(output,inverse_impulse);
convolution_time=linspace(min(out_time)+min(t),max(out_time)+max(t),length(convolution_result));
figure;
plot(convolution_time,convolution_result);
title('input plot after convolution');

William Rose 2024-2-27

@Paul is right, as usual. It is not true that

"If x(t)*h(t)=y(t) then x(t)=1/h(t) * y(t) where * is convolution and h(t) is the impulse response."

When I say DFT below, I mean the discrete Fourier transform, which you can compute with fft().

I would do the deconvolution in the frequency domain. To do this, you will need the frequencies of the S21(f) response to be the same as the frequencies of Y(f)=DFT of y(t). Then you can estimate X(f)=Y(f)./S21(f), and x(t)=invDFT(X(f)). But remember that the DFT assumes that your recording of y(t) represents exactly one period of a periodic signal. Your recording of y(t) has about 3.5 periods. So there will be a lot of high frequency "noise" in the DFT, due to the mismatch between the beginning and the end. This is why you use a window such as Hamming or Hann. If you apply a window to Y(f) before computing its DFT, then the X(f) and x(t) you get from deconvolution will be the input that gives the windowed signal. Another option is to clip y(t) so that it wraps around smoothly, i.e. so that you have exactly 3 cycles of the signal, not 3.5. You may also need to apply a linear adjustment, i.e. a kind of "tilt", so that the beginning and the end of the signal line up smoothly. Then you can apply the opposite tilt to the final x(t) which you get from deconvolution.

Ganesh Prasad 2024-2-28

Please see the S21(please change .txt to .s2p extension) and output waveform file(.xlsx) attached.Thanks.

Paul 2024-2-28

在 MATLAB Online 中打开

S21.txt

Taking a look at the data

copyfile S21.txt S21.s2p
S = sparameters('S21.s2p')
S = 
  sparameters: S-parameters object

       NumPorts: 1
    Frequencies: [1774×1 double]
     Parameters: [1×1×1774 double]
      Impedance: 50

  rfparam(obj,i,j) returns S-parameter Sij

The frequency data does not start at zero. I think if you're going to use the IFFT approach, you'll have to figure out how to extrapolate S21 to zero.

format short e

S.Frequencies([1 end])

ans = 2×1

1.0e+00 * 1.0000e+06 2.7000e+10

figure

semilogx(S.Frequencies,abs(squeeze(S.Parameters)))

The frequencies are not equally spaced (maybe they're spaced logarithmically?). Before taking using IFFT I think you'll have to do an interpoplation to an equally spaced frequency vector.

figure

plot(diff(S.Frequencies))

After those two issues are sorted out, you'll have to also account for the "upper half" of S21 in the frequency domain. Assuming that the impulse response is supposed to be real-valued, check this answer for a discussion on that topic.

I believe that all of these issues need to be addressed first to get the "full picture" of S21 before proceeding with the frequency domain approach suggested by @William Rose or with a time domain approach as you are attempting.

I didn't look at y(t), I suspect that there will be more work to do on that as well depending on decisions made on how you modify the S21 data.

There may be other options to to address this problem as well.

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Answer 1

William Rose 2024-2-28

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2085218-determining-the-input-from-the-output-using-ifft#answer_1418396

@Ganesh Prasad,

Here is a script that does the deconvolution in the frequency domain, using the ideas in my comment above. It also does what @Paul suggested: it interpolates and extrapolates S21(f) to the frequencies of the output signal's Fourier transform.

The script makes five figures, which are mainly to reassure me that everything is working as I expect. The final figure, copied below, shows the output and esitmated input. I am not saying it is perfect.

See comments in the script for details.

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Ganesh Prasad 2024-3-3

@William Rose Thank you for taking the time out and explaining in detail with the code.This will help me verify the results I got from the simulation.

@Paul Thank you for giving your valuable inputs to get the solution to the problem.

Thanks a lot and sorry for the delayed response.

William Rose 2024-3-3

@Ganesh Prasad, you're welcome.

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Determining the input from the output using IFFT

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