I have these 3 equations:

enter image description here

Now I want to calculate the function f(x).

The f(x) should like this:

enter image description here

Here a1-a7 are constant parameters.

Could someone tell me how to calculate the f(x)? Thank you very much.

  • $\begingroup$ In the Fourier domain, a convolution in the time domain maps into a multiplication in the frequency domain. Therefore a deconvolution maps into a division. And you see the danger with deconvolution comes when you have numerical data and a kernel that becomes small. You then divide noise data by a small divisor creating large errors. But as long as you have analytical functions this does not happen. $\endgroup$ – Daniel Huber Mar 3 at 11:01
  • $\begingroup$ In this case, you can see that a3 and a6 must be 0.3 and 0.5. a7 must be zero. Leaving the remaining parameters as symbols, Mathematica can compute the convolution. Match the 2 terms of the result with the 2 terms in your expression, and you are done (nearly). $\endgroup$ – mikado Mar 3 at 15:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.