[time-nuts] power spectrum of hard limiter output
jimlux at earthlink.net
Tue Jan 25 13:53:24 UTC 2011
On 1/24/11 1:19 PM, Magnus Danielson wrote:
> What are you *really* trying to achieve? 1-bit ADC at the end of a noisy
I have a GPS receiver front end (sampler) that normally one tests by
running GPS signals through it, acquiring and tracking the signals and
deriving SNR estimates, etc. , but we're in a situation where we don't
have either the back end processing or the GPS signals. We *do* have a
signal generator, so I was looking for some analytical expression(s)
that say, if you put in a tone with X SNR, this is what you should see
coming out of the sampler.
It's easy to do a sort of qualitative test (put in a big signal, see if
you get a square wave out), but it would be nice to be able to have a
way to make a quantitative measurement, particularly of the noise figure
& gain of the receiver. People have done a sort of ad hoc measurement
(hooking up a spectrum analyzer to the single bit digital output of the
sampler), but I was looking for something a bit more rigorous, but not
to the point where *I* wanted to grind out the pages of equations.. I
was hoping that someone else (e.g. Aronson) had gone through the exercise.
The interesting thing is that there *is* a fair amount of analysis of
the bandlimited signal(s) and noise into a hard/soft limiter into a
filter. However, there's not much on systems where there is a sampling
process as well (which aliases all those harmonics down, of course).
The more recent literature I was able to find tends to be of a more
empirical nature (e.g. the modeling/simulation/experimental results).
And that's fine (after all, Aronson says that simple closed form
solutions probably don't exist). I can crank out models with the best
of them, but, philosophically, if there is a nice *simple* analytical
approximation, that's nicer.
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