The Convolution and Deconvolution available from the Origin Analysis menu are limited in that:
[1]The Response dataset should be symmetrical
[2]The Response dataset must have an odd number of points
[3]The Response dataset should be smaller than half the signal dataset size
[4]No normalization is done (convolution or deconvolution)
[5]We include the bin index as the X
[2] and [3] are restrictions which can not be ignored. Ignoring [1] will result in positive and negative values that are shifted from each other. [5] can be completely ignored by simply deleting the Index[X] column that Origin creates. The effects of [4] simply change the Y scale and doing deconvolution followed by convolution (or vice-versa) - same response data - will cancel out the normalization problem.
Deconvolution can introduce some severe artifacts when the Signal contains any noise or the Response is broad in comparison to the Signal. Given this, Signal datasets should be smoothed before deconvolution and Response datasets should be 'narrower' than any features in the Signal dataset (this is only logical anyway).
While I didn't quite follow your procedure (convolution and deconvolution are worksheet procedures), if your data meets the restrictions above, you should be able to:
Convolute 'Signal' with 'Response' to get 'Convolution', then deconvolute 'Convolution' with 'Response' to get 'Signal'. Similarly, you should be able to deconvolute 'Signal' with 'Response' to get 'Deconvolution', then convolute 'Deconvolution' with 'Response' to get 'Signal'.
We will be re-writing the Convolution/Deconvolution code to use the NAG libraries which are less restrictive in their data requirements, so [1] through [5] will 'go away'.
(Note that the problems caused by deconvolution of noise and illogical Response peaks will remain.)
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deconvolution
Posted - 11/11/2002 : 12:52:30 PM
