recreating a time series from a subset of fourier coefficients

["Potgieter, Andries B" <Andries.Potgieter@dpi.qld.gov.au>]

Dear S-News,

I have the following question:

IF
 - X <- c(1, 3, 7, 4, 1)
 - Y <- fft(X)
 >  16.000000+0.000000i  -6.663119-3.665469i   1.163119+1.677599i   
 > 1.163119-1.677599i  -6.663119+3.665469i

then
recreating X from Y but only using the first 2 coefficients
 Y[3:5]<- 0
>  16.000000+0.000000i  -6.663119-3.665469i   0.000000+0.000000i   
> 0.000000+0.000000i  0.000000+0.000000i

thus

 Re(fft(Y,inverse=T)/5)
[1] 1.867376 3.485410 4.709017 3.847214 2.090983


My question is: Is this valid and is it the best way in recreating a original 
time series from only a subset of harmonics?

thanks
andries



                Andries Potgieter 
                Research Scientist
                Climate and System Technologies
                Emerging Technologies
                Delivery
                Department of Primary Industries and Fisheries

                Telephone 07  4688 1417  Facsimile 07  4688 1193
                Email andries.potgieter@dpi.qld.gov.au   
<mailto:andries.potgieter@dpi.qld.gov.au>Mobile 0408 715 514
                Website www.dpi.qld.gov.au  Call Centre 13 25 23

                Profitable primary industries for Queensland 

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