Generating Scalar Data from Complex Data

On Jan 27, 1:50 pm, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:
> On Sat, 26 Jan 2008 21:30:32 -0800 (PST), dbd <d...@ieee.org> wrote:
> >On Jan 24, 1:27 pm, "John E. Hadstate" <jh113...@hotmail.com> wrote:
>
> >> Is it possible to generate a scalar sampled data stream from a
> >> sampled complex data stream without losing information?
>
> >> For example, can I take complex data that was sampled at 100
> >> Hz. with a bandwidth of +/- 50 Hz around 0 Hz. and convert it
> >> to a scalar data stream that is sampled (effectively) at 200 Hz
> >> and preserve all the information between 0 and 100 Hz?
>
> >Take your complex data array:
> >real0, imag0, real1, imag1, real2, imag2, real3, imag3, ...
> >Multiply alternate pairs by -1:
> >real0, imag0, -real1, -imag1, real2, imag2, -real3, -imag3, ...
> >Interpret that array as reals:
> >real0, real1, real2, real3, real4, real5, real6, real7, ...
>
> >Since this is reversible, barring errors due to multiplying by -1, no
> >information is destroyed. It is equivalent to upsampling by 2 by
> >duplicating  each complex sample and complex demodulating by Fs/2
> >where Fs is the original complex sampling frequency, and taking the
> >real part. (Or inserting zeros and filtering by [1,1] then
> >demodulating, etc.)
>
>   (snipped by Lyons)
>
>
>
> >Dale B. Dalrymple
> >http://dbdimages.com
> >http;//stores.lulu.com/dbd
>
> Hi Dale,
>   your scheme is interesting.  I don't
> recall seeing this notion, this process, before.
> (I'm gonna study this, as time allows.)
>
> Dale will you tell me what you mean by the
> words "complex demodulating"?
> Thanks.
>
> [-Rick-]

Rick

"Complex demodulation" is simply multiplying by a complex exponential
time sequence. "Demodulation' from it's use to bring a frequency band
of interest to DC before filtering and desampling in receivers and
spectrum analyzers. harris uses "full complex heterodyne" in his
"Multirate DSP" book.

Dale B. Dalrymple