[time-nuts] power spectrum of hard limiter output

[Magnus Danielson]

On 24/01/11 07:39, Bruce Griffiths wrote:
> 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

http://archive.numdam.org/ARCHIVE/RSMUP/RSMUP_1969__42_/RSMUP_1969__42__1_0/RSMUP_1969__42__1_0.pdf

http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA425520

... found using "hard limiter autocorrelation sine" in Google.

Cheers,
Magnus