 Brian P. wrote on Mon, 5 Mar 2007 16:05:09 -0500:

That Analog Devices AD9235-65 looks like it’s good if you want to
sample at something like the USRP is doing right now - 64MHz. So what
you’d be looking at is an oscope with a 500MHz bandwidth and a 64MSPS
sampling rate. You could possibly double that if you did some
cascading of the ADCs and used the opposite edge of the clock to also
clock into a different ADC - giving you (effectively) double the
samples per second.

If one was to shift the second ADC by 90 degrees to the clock instead
of 180, wouldn’t one be gaining I/Q data aswell as increase the
effective sampling rate?

Nos

On 3/7/07, [email protected] [email protected] wrote:

If one was to shift the second ADC by 90 degrees to the clock instead
of 180, wouldn’t one be gaining I/Q data aswell as increase the
effective sampling rate?

I found a post on dsprelated.com that can help. I will post relavent
information here.

– snip –

I (vaguely) heard that sampling complex-valued data does not abide by the
Nyquist rate criteria, i.e., the sampling rate fs can go lower than Nyquist
rate and it still can avoid aliasing and reconstruct perfectly…

Is that true?

Yes. Real sampling at Fs samples/second provides a “usable” bandwidth
of Fs/2 Hz while complex sampling provides a usable bandwidth of Fs Hz
at the same sample rate.

Any theory behind it?

Yes. Use two pieces of knowledge: a) the Fourier transform property
that H(f) = H*(-f) (this is known as “Hermitian symmetry”) for a real
signal h(t), H(f) = F[h(t)], and b) the fact that sampling can be
viewed in the frequency domain as replicating the band from -Fs/2 to
+Fs/2 every Fs Hz.

More simply, a real signal has bandwidth from 0 to Fs/2 available, while
a complex signal has bandwidth from -Fs/2 to +Fs/2 available.

## As I recall, Richard Lyon’s book “Understanding Digital Signal Processing” (2nd ed.) discusses this phenomenom at great length.

% Randy Yates
– snip –

Nos

Brian

On 3/8/07, [email protected] [email protected] wrote:

Fascinating subject. I think I’d very much like to experiment with

It becomes a very tricky subject and is very susceptible to clocking
and phase noise.

If one puts an ADC at 0, 90, 180 and 270 degrees on the clock, one
should be getting four times the sample rate and twice the bandwidth
of just one ACD, yes? I don’t see any reason why it wouldn’t work, but
I’ve become used to surprises.

If you have a sample clock running at Fs, you effectively have Fs/2
bandwidth for real signal sampling. If you add in both rising and
falling edges of the clock (0 and pi phase shifts), you can double
your Fs to 2Fs and double your sampled bandwidth to Fs. Now, if you
do the peak and trough of such a thing, you end up with 4 points you
are sampling, doubling your previous sampling rate and doubling your
previous bandwidth to be 2
Fs - where Fs was your original sampling
frequency.

Both are an increase of 4x.

The problem I see with the above is this: to get accurate clocking,
you need a sharp edge to take the sample. A square wave works very
nicely for this. To get the 180 degree shift clock, you simply take
the falling edge of that square wave. This is relatively simple to do
and is used in many places.

When generating the 90 and 270 degree shifts, that requires a little
bit of problem solving since you don’t really have a clear
transitioning point in the middle of those flat tops to be able to
take an integral or derivative of such a wave.

Now, if you were to take a fixed frequency sinusoidal clocking source
and run it through a capacitor, the output of this capacitor should be
at a 90 degree phase shift from the original signal. If you then sent
those two clocking sources through a squaring circuit, you could
possibly get a pretty decent set of sources out of that. NOTE: I have
never done this and the thought just popped in my head - I am sure it
is very rudimentary and quite possibly does not even work.

Either way, to fully exploit that, you would have to send those
through some inverting buffer that would give them all rising edges
where they needed to be instead of both rising and falling edges. As
you can see, with all the different stages the signals have to go
through - there is a good amount of uncertainty that comes with the
phase delays of each path which all have to be matched. Significant
engineering time would have to go into the modeling and simulation of
this along with building, debugging and late night bouts of
frustration.

As another note, there may already be some discrete chips that perform
such phase shifts with very low phase noise. Let me know if you find
anything.

I wonder if some sort of beat frequency would emerge if I ran two ADCs
at different sample rates on the same signal, and what for the beat
frequency would manifest in… Or for that matter, if one used ACDs
the respective number of bits of each would divide into an infinite
decimal representation when the peak-to-peak voltage of each is equal.
By manipulating parameters like these in real-time one might be able
to gain a lot of information from repetitive signals. Maybe even do a
“derivate scan” at whatever precision you managed to manipulate your
clock at…

You lost me here.

Noise is a problem smashing the mathematical neatness into bytes, but
I seem to remember something about ‘sample aperture’, I think it was.
I suspect it does some sort of averaging of the signal, so this window
width of the sample would provide some sort of critical frequency
too… Maximum undersampling rate, maybe?

Aperture jitter is the delay that it takes your ADC to take it’s
This is usually pretty small, but can cause some problems with there
is a very high IF and you are under sampling.

Usually this is significantly less than your input analog bandwidth
anyway.

I’m going to start looking into these issues, but if you happen to
know the answers please point me to them. “Understanding Digital Signal Processing” by Richard G. Lyons (ISBN:
0-13-108989-7) spends a significant amount of time discussing periodic
sampling in Chapter 2. You can probably pick up a whole heck of a lot
of information from there.