[time-nuts] power spectrum of hard limiter output

[Bruce Griffiths]

jimlux wrote:
> 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...)
>
See:

http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4101285

Bruce