Complex baseband signal. Inphase-Quadrature data

Hello Randy,

Then, could you provide a reference/s by which complex sampling is defined?

I am interested in understanding well the relationship between a REAL
signal (the signal which flights over the air), complex sampling and
Nyquist theorem.
I am interested in practical cases, since I seem to understand that complex
sampling is carried out for a real signal that initially meets the even
parity in the frequency domain (its module has a simmetry respect positive
and negative frequencies). For example, many receivers implement I/Q
demodulation obtaining a baseband representation of a passband signal
(e.g., QAM demodulation).

Cheers,

M
>On 12/05/2010 07:54 AM, MRR wrote:
>> Thanks a lot for this debate.
>> I continued this issue in wikipedia and the article "sampling" have
been
>> modified. One of the editors has added "complex sampling", which may be
>> useful for understanding how the demodulation with complex baseband
>> representation is carried out.
>>
>> Here you are the link:
>> http://en.wikipedia.org/wiki/Sampling_%28signal_processing%29
>>
>> Cheers,
>>
>> M
>
>The definition of complex sampling in that article is
>not correct. The real and imaginary components of a
>complex signal are not required to be related. Complex
>sampling is not necessarily of Hilbert transform pairs.
>
>--Randy
>
>

On 12/05/2010 11:49 AM, MRR wrote:
 > Hello Randy,
 >
 > Then, could you provide a reference/s by which complex sampling is defined?

I couldn't find a good one on my bookshelf. It may be one of those things
that are so basic folks don't think about defining it precisely.

My best shot would be this:

   Complex Sequence: A sequence of samples x[n] where x[n] \in C and
   n \in Z.

Note that "\in" is the set "element of" operator, and "C" is
the set of complex numbers and "Z" is the set of integers.

 > I am interested in understanding well the relationship between a REAL
 > signal (the signal which flights over the air), complex sampling and
 > Nyquist theorem.

 > I am interested in practical cases, since I seem to understand that complex
 > sampling is carried out for a real signal that initially meets the even
 > parity in the frequency domain (its module has a simmetry respect positive
 > and negative frequencies). For example, many receivers implement I/Q
 > demodulation obtaining a baseband representation of a passband signal
 > (e.g., QAM demodulation).

Since there are very few (if any, but that could probably be debated)
real-world complex signals, complex signals are derived from real
signals as you have stated, usually (at least in signal processing)
either by Hilbert transform or by quadrature downconversion.
-- 
Randy Yates                      % "My Shangri-la has gone away, fading like
Digital Signal Labs              %  the Beatles on 'Hey Jude'"
mailto://yates@ieee.org          %
http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO

Nice to see that 2 years after this question can be completed by myself.
Hope it helps to someone else.

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