Awesome explanation about quadrature sampling by Matt Ettus

Normally, to sample a BW of X, you need to sample at 2X.  So what can you do if you want to increase the BW sampled, but can't increase the sample rate?  If, instead, you can throw a second sampler at it, you use quadrature sampling.

If your BW of interest is from w to w+2x (a BW of 2x), you mix the signal with a sine of frequency w+x (i.e. the center frequency).  This will make the components of the signal at w+x go to a frequency of 0.  The components from w will mix down to 0-x, and those from w+2x will mix down to 0+x.  Since +x and -x are really the same, the BW is from 0 to X, and all the components now will get through a sampler sampling at rate 2x.

The problem is that 0-x and 0+x alias onto each other, since you can't tell the difference between negative and positive frequencies.

So instead of just mixing with a sine wave and sampling, you also mix with a cosine wave, and sample it with the other sampler.

 

Now you have 2 sampled signals, each at rate 2x, each with components from -x to +x.  Independently the negative and positive components are indistinguishable.  By intelligently using complex numbers and BOTH samples, the negative frequencies can now be separated from the positives.

Thus you have sampled a BW of 2X by using 2 samplers of rate 2x, instead of using one at a rate of 4X.
 

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