Fast Fourier transform to perform deconvolution with log time

I have two 1-D data with x-axis is log(t) but not t below with my data,

I have trouble using fft to perform R(z) = da(z)/dz ⊗−1 (deconvolution) w(z). to get R(z)

I tried a=fft(da/dz) and w=fft(wz) and R=a./w and using ifft(R) to get R(z) , but result is quite strange

below is the result R(z) I shold get.

can anyone told me how to got R(z) by deconvolution using fft and ifft?

Answer 1

[Wolfgang]

Hello larry liu,

it seems like I have exactly the same problem. I'm trying to do the deconvolution of a thermal impedance curve and I'm stuck with the deconvolution part.

Top left is the testcurve generated from discrete R and C values

Top right are the time constants of these RC-values, therefore I expect some curve at the output that looks at least somehow similar to these stems.

The bottom plots show the two curves which need to be devonvolved with each other.

This is the result I get. It makes absolutely no sense:

Did you find a solution?

[larry liu]

Sorry I missed the message

I used the "Bayesian deconvolution" instead, maybe you can try it.

reply if any question!

[Wolfgang]

Hello Larry,

I'm still fighting with this problem (its just one of many small side projects).

I was looking for a working implementation of the Bayesian deconvolution, but I couldn't find any.

Do you have a working Matlab Code for this?

I also added the code I'm currently working with. I uses RC values I provided by Nexperia to build a simulated Z_th curve. This is the starting point for the NID stuff.

Later this shall work on measurement data, but there I don't have any clue which RC-values to expect. That's why I started with measurement results done by Nexperia.

[Savas Kaya]

Wolfgang & Larry Liu:

Did you ever get a solution/closure on this deconvolution problem?

We are also dealing with the exact same problem and our 1D Richardson deconvolution cannot resolve the expected peaks. I do get the 3 peaks on both real space and Transform approaches, but neither the two approaches agree (they should) nor the peaks are on right places (should have three peaks at ln(10) = 2.3026, ln(1)=,0 and ln(0.1)=-2.3026.

Any ideas and feedback are welcome.

I am atatching both the two versions of our MArlab script as well as the 3 papers I followed to get here.

[高飞 支]

hello Savas

How did you handle the response function W? How did you transform the function w into a matrix? I found a Bayesian iteration formula, but it involves a matrix W, not the function w.

[Wolfgang]

Hello Savas,

sadly I have to admit that I did not further investigate on the problem as I got distracted on other topics.

Nevertheless I'm still looking for a solution to get it working.

[yicong]

How do you solve this problem? Could you give some other insight about this matrix W?