[time-nuts] power spectrum of hard limiter output

[Magnus Danielson]

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