Bart Hazes schrieb: ...
W.r.t. Kay's reply I think the argument does not hold since it depends on how badly the data is truncated. E.g. truncated near the limit of diffraction will give few ripples whereas a data set truncated at I/SigI of 5 will have much more servious effects.Bart
Bart,if you truncate at the limit of diffraction (i.e. where there is no more signal) you will not get any ripple at all !
Of course, if you truncate at a resolution where there is significant signal (and I do agree with you in that respect: many people truncate their datasets at too low resolution) there _will_ be Fourier ripples. However, a ripple is never as high than the peak itself.
To get a quantitative picture of the worst-case scenario, consider the following: truncation means multiplication of the data with a Heaviside function (that is 1 up to the chosen resolution limit, and 0 beyond). In real space, this translates into a series of ripples, arising by convolution of the true electron density with the Fourier transform of the Heaviside function. The Fourier transform of a one-dimensional Heaviside function is the function sin(x)/x . Convolution with sin(x)/x has the effect of a) broadening (or "smearing") the true electron density, resulting in a low-resolution electron density map instead of the true one b) adding ripples at certain distances (which can be calculated from the resolution) around each peak. The first negative ripple has an absolute value of less than 1/4 of the peak height, and the first positive ripple about 1/8 of the peak height.
So in the worst case (one-dimensional truncation of data) my estimate of 12% was wrong - I estimated the height of the first positive ripple whereas Klemens reported the first negative ripple!
On the other hand, if I remember correctly, the Fourier transform of the 3-dimensional Heaviside function (a filled sphere) is a Bessel function that has ripples which (I think) are lower than those of the one-dimensional Heaviside function. Surely somebody knows the function, and its peak heights?
best, Kay -- Kay Diederichs http://strucbio.biologie.uni-konstanz.de email: [EMAIL PROTECTED] Tel +49 7531 88 4049 Fax 3183 Fachbereich Biologie, Universität Konstanz, Box M647, D-78457 Konstanz
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