How to obtain the system response from initial signal and final signal? Using Convolution or deconvolution!

Dear Researchers and Matlab Community,

I have a query regarding to obtain the system response.

In order to obtain the correct result from scatterings, I divided the signal using %Sc = S./(repmat(Sref,size(S,1),1));

as given below:

My question is how can I get the system response, since I have both Y and X, how can I get H, I read about Convolution or deconvolution.

I need guidance to obtain the system response.

angle = -180:1:180-1;

Angle_ref = 5;

S = input (2D signal) % attached

[val_min,i_ref] = min(abs(angle - Angle_ref));

Sref = S(i_ref,:);

Sc = S./(repmat(Sref,size(S,1),1));

Your comments and suggestions/solution will be highly appreciated.

[Amjad Iqbal]

@Chunru I need your suggestions, to obtain the impulse or the system response (H), where Y = Sc, and X = S.

[Chunru]

Can you describe what your input and output are? Are the 2D spatial signal?

[Amjad Iqbal]

@Chunru

Yes, These are the 2D spatial signals. Input is "S" obtained from scatterings.

In .mat file there are two variables S and S_c input and output respectively.

Logically, it doesn't require in my work to divide "S" with "Sref" to obtain Sc (it was additional step).

as given below, its due to caliberation from system I used to obtain the scatterings.

Sc = S./(repmat(Sref,size(S,1),1))

That's I was trying to get this system response.

[Chunru]

Both S and S_c has two dimensions. What are thes two dimensions? How are they connected by system response? Please give some background information. Otherwise it is all guess-work.

[Amjad Iqbal]

@Chunru

Attched is the script and all the necessary parameters are given in that. Mag_phase contaid the scattering matices to be used in line in 5

S_rect = 10.^(mag_freq/20).*exp(1j*phase_freq*pi/180);

Line 34 - 38 are reffering to adjust the system response to obtain the correct result. Normally, in image focusing this division is not required. This may comes from system caliberation.

Please if you need any further information, I'm at your disposal. Thank you.

[Chunru]

My question is how can I get the system response, since I have both Y and X, how can I get H, I read about Convolution or deconvolution.

In time domain, Y = conv(H, X)

In Freq domain, Y = HX

So an estimate of system response in frequency domain is H = Y/X. But it is tricky when X=0. So Y and X need to be estimate with some smoothing function.

[Amjad Iqbal]

Do you think the system response might be very non-linear?

As per above equation I obtained such response, it should me rect or sinc, but I guess may be due to X has more zeros. or any suitable solution to find the reasonable system response!

[Chunru]

One way is to build a model of the system with some parameters and then estimate the parameters from data. This requires background information about the problem you want to solve.