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.

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.

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.

Image Source : http://w5vwp.com/blog/wp-content/uploads/quaddet.jpg

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