[time-nuts] power spectrum of hard limiter output
Magnus Danielson
magnus at rubidium.dyndns.org
Mon Jan 24 06:01:01 UTC 2011
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.
Cheers,
Magnus
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