Strange deconvolution results

[PaulPaul]

Homework Statement

Hi. I don't understand my results when I deconvolve two non-negative peaks. I also get a peak but it is fallowed by a negative "valley". Can devonvolution of two positive graphs give graphs with negative parts?

Homework Equations

In this case I deconvole two gamma variates:
f(t) = a(t-to)^b exp[ -(t-to)/c ] step(t-t0)
g(t) = d(t-t1)^k exp[ -(t-t1)/m ] step(t-t1)

The Attempt at a Solution

I use MATLAB's discrete Fourier tranformation function and simply divide without filtering (what filter would I use? Is there noise in a sampled analytical function?) I've also tried changing sampling frequency and the window of the function = the negative dip stays there! I've also used Singular value decomposition to do the deconvolution- also I get a negative valley. Where does this come from? Does deconvoluion have a unique solution?

thanks.

 

[Jhero]

Hi there, thank you for your post. It seems like you are trying to deconvolve two non-negative peaks using MATLAB's discrete Fourier transformation function. However, you are getting a negative dip in the resulting graph. This can be confusing and may lead to questions about the validity of the deconvolution process.

Firstly, it is important to note that deconvolution is a mathematical process that aims to separate a signal into its individual components. In your case, you are trying to separate the two gamma variates. However, deconvolution is not a perfect process and there are limitations to its accuracy. In some cases, deconvolution may not give a perfect result and can introduce artifacts or errors in the resulting graph.

In your case, the negative dip in the resulting graph could be due to the limitations of the deconvolution process. It is possible that the two gamma variates are not perfectly separable and the deconvolution process is introducing this artifact. It could also be due to noise in the sampled analytical function, which can affect the accuracy of the deconvolution process.

To improve the accuracy of the deconvolution process, you can try using different filters or window functions to remove noise from the signal before deconvolving. You can also try adjusting the sampling frequency to see if it improves the result.

In general, deconvolution does not have a unique solution and the accuracy of the result depends on various factors such as the quality of the data and the mathematical methods used. It is important to carefully analyze the results and consider the limitations of the deconvolution process.

I hope this helps to clarify your doubts. Keep exploring and experimenting with different methods to improve the accuracy of your results. Good luck!