Started by March 20, 2011
```Hello,

I'm not sure I fully grasp quadrature sampling.  My idea of what quadrature
sampling is (from a communications perspective) this:

So if I have a signal x(t) = sin(2*pi*f*t) + cos(2*pi*f*t) and I sample it
with my two ADCs that are 90 degrees out of phase at a a rate f.  Can I
fully recovery x(t)?  I can't think of a reason why not.

Also, if my understanding of quadrature sampling is correct, is there a
difference between quadrature sampling at a rate fs and normal sampling at
a rate 2*fs (assuming the sampled signal is complex)?

```
```On Mar 20, 7:14&#2013266080;am, "colsandurz45" <dwwkelly@n_o_s_p_a_m.gmail.com>
wrote:
> Hello,
>
> I'm not sure I fully grasp quadrature sampling. &#2013266080;My idea of what quadrature
> sampling is (from a communications perspective) this:
>
> quadrature (Q). &#2013266080;The two ADCs sample 90 degrees out of phase.
>
> So if I have a signal x(t) = sin(2*pi*f*t) + cos(2*pi*f*t) and I sample it
> with my two ADCs that are 90 degrees out of phase at a a rate f. &#2013266080;Can I
> fully recovery x(t)? &#2013266080;I can't think of a reason why not.
>
> Also, if my understanding of quadrature sampling is correct, is there a
> difference between quadrature sampling at a rate fs and normal sampling at
> a rate 2*fs (assuming the sampled signal is complex)?

"Quadrature sampling" is a term that can refer to a number of
concepts. Try googling, the first 50 hits give discussions of a number
of these concepts.

Dale B. Dalrymple
```
```On 03/20/2011 10:14 AM, colsandurz45 wrote:
> Hello,
>
> I'm not sure I fully grasp quadrature sampling.  My idea of what quadrature
> sampling is (from a communications perspective) this:
>
> quadrature (Q).  The two ADCs sample 90 degrees out of phase.
>
> So if I have a signal x(t) = sin(2*pi*f*t) + cos(2*pi*f*t) and I sample it
> with my two ADCs that are 90 degrees out of phase at a a rate f.  Can I
> fully recovery x(t)?  I can't think of a reason why not.

If you have a real signal, you can either use one ADC sampling at
twice the highest frequency or two ADCs sampling at the highest
frequency if you do some manipulation of the sampling and/or input
signal. The scenario you described falls under the former.

> Also, if my understanding of quadrature sampling is correct, is there a
> difference between quadrature sampling at a rate fs and normal sampling at
> a rate 2*fs (assuming the sampled signal is complex)?

"Quadrature sampling" is the process of sampling a complex signal in
rectangular form. That is, if z(t) = x(t) + i*y(t), then z[n] = x[n] +
i*y[n]. I[n] is x[n] and Q[n] is y[n].

There are a myriad of ways to derive a complex signal, e.g., a complex
mix to an IF, a complex mix to baseband, sampling the same signal at
different sampling phases, etc.

I have a suprise for you (at least it was a surprise for me when I
realized it): sampling ALWAYS gives you a bandwidth of -Fs/2 to +Fs/2,
whether real or complex. However, real sampling forces half of that
bandwidth to be redundant, or in other words, to carry no extra
information. Complex sampling allows the entire bandwidth to carry
information.