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fengyuntao
USA
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 Posted - 01/30/2006 : 10:00:12 PM
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Origin Version (Select Help-->About Origin): 7.5
Operating System: Windows XP Pro
I am a new Origin user trying to solve some deconvolution problem. I checked the related topics in the forum and the example provided by Origin but I got confused with the results I got, the porblems are as follow:
I tried to run the deconvolution example provided by Origin 7.5. Using the Signal and Response I could successfully get the Conv signal, however, whenever I tried to deconvolve Signal from Conv and Response I could not get the same results as the example got, though the results were very close. What confused me was that when I copy Conv and Response to a new file and deconvolve directly (meaning not to convolve Signal and Response first in the same file), the result does not make sense, it looks like some random positive and negative numbers mixed together and does not follow any curve. I made up a lot of simple and complicated convolved signal and response function, but none of the deconvolved signal made sense.
I also tried to deconvolve Response from Conv and True signal of the same length using the script command method introduced in the forum, I was able to make it run and get some results, but the results were not even close. I understand that this process involves FFT and inverse FFT so may not be accurate, but I do expect to get a result which can make a little bit sense.
I don't know if I made myself clear, but any comments regarding deconvolution will be highly appreciated. Thanks for your attention.
Frank
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easwar
USA
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Posted - 01/31/2006 : 10:25:13 AM
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Hi Frank,
First of all deconvolution does not always provide the right result due to the nature of the transformation. See this comment from Wolfram for example:
"Deconvolution is ill-posed and will usually not have a unique solution even in the absence of noise"
http://mathworld.wolfram.com/Deconvolution.html
Now, the way deconvolution is implemented in Origin is to compute the FFT of the (convoluted) signal and the FFT of the response, then dividing the first by the second and then performing an inverse FFT. The division is susceptible to issues such as division by very small numbers even in the absence of significant noise in the signal or response curve etc.
The menu item in Origin in 7.5 also assumes that the response function is symmetrical and is odd-numbered in length etc. If you use the NAG library to perform the deconvolution with code such as in this post http://www.originlab.com/forum/topic.asp?TOPIC_ID=3151
you do not have those limitations, but still there is no guarantee you will get a reliable/consistent result.
Easwar
OriginLab
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Problems regarding deconvolution