[time-nuts] power spectrum of hard limiter output

[jimlux]

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
> channel?
>


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.