Complex samples real samples

I have a simple question regarding equivalent complex and real sequences.

I know that by sampling in quadrature (I and Q complex samples) you can
satisfy the Nyquist criteria at the sample rate (fs) and if I took real
samples only and sampled at 2fs, then I should get equivalent power
spectra in the bandwidth 0<f<1/fs with the real sequence's power spectrum
aliased in the bandwith 1/fs<f<2/fs.

It seems there should be a way to transform the two sequences. I tried
forming a real sequence from a complex sequence by making the even
elements of the real sequence equal to the real elements of the complex
sequence and the odd elements of the real sequence equal to the imaginary
elements of the complex sequence. The real sequence is then interpreted as
having been sampled at 2fs, but it seems to have additional aliases I
didn't expect.

Is there a straightforward way of transforming the two sequences to have
common power spectra from 0<f<1/fs? The simple way I tried is close, but
not quite there.

Thanks.

fizzix wrote:
> I have a simple question regarding equivalent complex and real sequences.
> 
> I know that by sampling in quadrature (I and Q complex samples) you can
> satisfy the Nyquist criteria at the sample rate (fs) and if I took real
> samples only and sampled at 2fs, then I should get equivalent power
> spectra in the bandwidth 0<f<1/fs with the real sequence's power spectrum
> aliased in the bandwith 1/fs<f<2/fs.
> 
> It seems there should be a way to transform the two sequences. I tried
> forming a real sequence from a complex sequence by making the even
> elements of the real sequence equal to the real elements of the complex
> sequence and the odd elements of the real sequence equal to the imaginary
> elements of the complex sequence. The real sequence is then interpreted as
> having been sampled at 2fs, but it seems to have additional aliases I
> didn't expect.
> 
> Is there a straightforward way of transforming the two sequences to have
> common power spectra from 0<f<1/fs? The simple way I tried is close, but
> not quite there.

The imaginary parts of complex samples are taken at the same instant as 
real parts. Naming alternate samples "real" and "imaginary" works in 
certain circumstances, but that's only a sometimes useful fiction.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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