# Re: R-alpha: What we're up to ...

Bill Simpson (wsimpson@uwinnipeg.ca)
Tue, 11 Feb 1997 09:04:03 -0600 (CST)

```Date: Tue, 11 Feb 1997 09:04:03 -0600 (CST)
From: Bill Simpson <wsimpson@uwinnipeg.ca>
To: Ross Ihaka <ihaka@stat.auckland.ac.nz>
Subject: Re: R-alpha: What we're up to ...

>
>   2.	Complex arithmetic.  This has finally hit the top of the
> 	priority heap.
know a lot about linear systems theory and system identification, and I
know the transfer function H(s) is a function of complex freq s.  HOWEVER
in practice even in FORTRAN which does have innate complex variables,
people  split the data into real and imaginary parts.  In fact all the
fastest FFTs I know about do this.  Moreover, are there people out there
who have time (or space) domain data that are complex?  Doesn't almost
everyone have real data?

BTW for real data, doing a FFT of two arrays, one real and one complex
consisting of zeros is dreadfully inefficient (not sure; is this what R
does now?). There are very old methods of doing FFT of real data by
packing TWO real arrays into the real and
complex input, and then separting out the results.  That will will be
about twice as fast though to me distastefully kludgy.  The better way is
to use a REAL FFT such as published by Sorenson in the 1980s.  For C code,
see
http://www.spektracom.de/~arndt/fxt/fxtpage.html
I translated Sorenson's real fft to C, and I could also do the IFFT (never
had a need so never did it).

Perhaps a parallel pair of functions
rfft
rifft
would be handy.

Just curious about the need for complex variables.  Maybe the only
motivation is to be compatible with Splus.

Bill Simpson

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