[time-nuts] power spectrum of hard limiter output

[jimlux]

On 1/23/11 10:01 PM, Magnus Danielson wrote:
> Jim,
>
> On 24/01/11 02:35, jimlux wrote:
>> I'm looking for a reference that gives the power spectrum of the output
>> of a hard limiter (1 bit thresholder) with band limited noise and a
>> single sinusoid.
>>
>> At high SNR, the output of the limiter is basically a square wave at at
>> the input frequency, but as the SNR decreases, it starts to act like a
>> soft limiter with a gaussian characteristic, so what is the power
>> spectrum of the output?
>
> It goes towards sine as I recall it. The gaussian noise rubs of
> overtones. Gardner describes this in his PLL book. Setting up a nice
> sawtooth detector is no good when seeing bad noise, as it will degrade
> into a sine-detector anyways, so using a multiplier is better for those
> conditions as you get a more stable property.
>
> Another approach of understanding is to consider that when the gaussian
> noise is sufficiently high it will start interpolate on the slope of the
> sine and as you add more noise more and more of the sine would linearize
> until you come to the point where it is linear. Soft-clipping will
> indeed be similar.
>
> I haven't seen a spectrum plot, but simulation in spice should be
> trivial. Setting up a sine + noise, comparator and then a low-pass
> filter should be a trivial SPICE setup. It does not take much
> imagination to see that the spectrum will migrate from that of a square
> over to that of a sine. It will loose power in those overtones.
>

oh, yes.. I did the simulation, and modeled the aliasing of the 
overtones and all..

I was looking for a reference to cite (you know how it is.. measure it 
yourself and it's something *you* did.. but cite someone who ground 
through it before, and it's worth a lot more...)