Re: Complex to 2x real - how?

Jerry Avins <jya@[EMAIL PROTECTED]
> writes:

> John wrote:
>> On Oct 9, 5:39 pm, dotter <dot...@[EMAIL PROTECTED]
> wrote:
>>> Hi,
>>> I'm struggling with how to convert a complex data stream into a real
>>> stream with the same bandwidth and twice the sample rate.
>>>
>>> How could this be accomplished?
>>> Thanks!
>>
>> 1. Interpolate by 2
>> 2. Mix to new sample rate / 4
>> 3. output = real part of (2)
>
> You lost me.
>
> If the signal is presented as C[n] = {Re(C([n]) + j*Im(C([n])}, just
> output Re(C([n]) and Im(C([n]) separately at the old rate. I'm at a
> loss, though, to guess how C[n] might have originated.

Hi Jerry,

All he's doing is this: 

  1. interpolating by 2 gets the sample up to 2*Fs

  2. Mix to new sample rate (2*Fs) / 4: this ****fts the
  spectrum by Fs / 2, so that what was at -Fs/2 to 0 is
  now at 0 to Fs / 2, and what was at 0 to Fs / 2 is
  now at Fs / 2 to Fs. Since the new sample rate is
  2*Fs, Fs is the highest frequency available.

  This preserves the information that was in the
  negative frequencies of the old complex signal
  in the positive frequencies of the new real
  signal.

  3. The spectrum in 2 was still complex, i.e., 
  potentially non-symmetrical. This step makes it
  symmetrical.

The bad thing about this approach is that it inverts
the spectrum, as seen by the step 2 explanation.
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