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generic convolution integral  (Genovis Inc)
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Genovis Inc generic convolution integral
Comparing electron density with its autocorrelation function demonstrates that P ( u ) reveals the interatomic distances. The centrosymmetric nature of the interatomic distance vector map (Patterson map) in contrast to the electron density map becomes obvious. We also discover that, as a result of the <t>convolution,</t> the Patterson peaks are twice as broad as the electron density peaks ( cf . purple arrows).
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Comparing electron density with its autocorrelation function demonstrates that P ( u ) reveals the interatomic distances. The centrosymmetric nature of the interatomic distance vector map (Patterson map) in contrast to the electron density map becomes obvious. We also discover that, as a result of the convolution, the Patterson peaks are twice as broad as the electron density peaks ( cf . purple arrows).

Journal: Journal of Applied Crystallography

Article Title: Deconvoluting Patterson

doi: 10.1107/S1600576725006569

Figure Lengend Snippet: Comparing electron density with its autocorrelation function demonstrates that P ( u ) reveals the interatomic distances. The centrosymmetric nature of the interatomic distance vector map (Patterson map) in contrast to the electron density map becomes obvious. We also discover that, as a result of the convolution, the Patterson peaks are twice as broad as the electron density peaks ( cf . purple arrows).

Article Snippet: Briefly, in the generic convolution integral (using as the convolution operator) for two different functions f ( r ) and g ( r ), we replace g ( r ) with g (− r ) which changes the second integrand to g ( r + u ) and the convolution into a correlation: Next, we substitute ρ for both g and f (same function, thus ‘auto’ in correlation).

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