On Jun 30, 1:43*pm, "BobW" <nimby_GIMME_SOME_S...@roadrunner.com>
wrote:
> "Jerry Avins" <j...@ieee.org> wrote in message
>
> news:b3s2m.2448$066.1548@newsfe08.iad...
>
>
>
> > BobW wrote:
> >> "Jerry Avins" <j...@ieee.org> wrote in message
> >>news:bfq2m.2441$066.810@newsfe08.iad...
> >>> BobW wrote:
>
> >>> * ...
>
> >>>> I found the answer. It was in the last place I looked.
> >>> Almost inevitably. Having found it, why look further?
>
> >>> * ...
>
> >>> Jerry
>
> >> Yes. I was merely trying to add a little bit of humor to this
> >> otherwise-dry newsgroup.
>
> > It alternates. Sometimes the humor gets laid on thick. (When I attempt it,
> > it often falls flat.)
>
> >> I sense that this technique of packing real data samples into the
> >> imaginary part of the input to the FFT is rather uncommon. Is that your
> >> take, too?
>
> > No. The technique seems to be widely known, but rarely needed. There are
> > real-to real FFT libraries available that do the scut work for the user,
> > as good libraries should.
>
>
> I certainly have found many real-to-real FFT routines, but the one that's
> available for my microcontroller merely stuffs zeros into the imaginary data
> input locations and then returns the magnitude of the outputs.

and, before the magnitude operation, you'll have a buffer of complex
data of which has its second half a complex-conjugate reflection of
the first (or "zeroth") half, with the exception of the DC and Nyquist
bins (but both of those will have 0 in their imaginary part). So a
unique set of N numbers gets inversibly mapped to another set of N
numbers.

>
> This particular technique, described by Mr. Lyons, puts the real data input
> samples into the imaginary inputs (rather than just setting them all to
> zero). The advantage is that the input data buffer size can be cut in half
> (for a particular input data set).
>
> Is it your experience that the "Lyons" technique is commonly used?

i dunno if Rick takes any original credit for this technique in his
book but it likely is either one of two methods; one where the real
parts of the N/2 FFT are comprized by the even-indexed samples from
the length-N real data and the odd samples go into the imag parts.
and then you detangle the output of the FFT (by investigation into how
the DFT would behave with this). the other method puts the second
half into the imaginary parts and the first (or "zeroth") half goes
into the reals. and then detangle the output.

r b-j