Today I read a Chinese paper about the “Function Data Analysis” and I was greatly amazed at what he described in the paper. Currently I’m not familiar with functional data at all, but he told us such a kind of “data” was just the result of applying a (some) smoothing function(s) to the original discrete observations, so the sample points became continuous (actually they became functions). These smoothing functions might either be Fourier transformations or B-splines.
I wonder whether there are some rules about the choice of smoothing functions, because if there aren’t any, the functional data will be rather free, and I cannot believe such a kind of data can really represent information behind these discrete data points: who knows what happens between two observations?! Only my naive ideas…
I read your chinese blog long time ago. That is so great. And today I accidentally found this entry.
And when I saw “Keep on Fighting”m, I know it is our R-expert. 
One of my college askes me to discuss the FDA with him next Monday. So if we have some outputs, I will come back here and reply you something.
Oh. another issue is, can you also send me the Chinese paper you mentioned in your entry? My Chinese is always better than English.
Thanks in advance!
The title and journal of the article can be found here: http://yihui.name/cn/2007/12/functional-data-analysis/