On 24/01/11 21:32, jimlux wrote:
On 1/24/11 11:44 AM, Magnus Danielson wrote:
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.
Excellent.. I had found the Aronson paper (wherein he effectively says
"there's no simple analytical expression".. that's nice and justifies
doing it by numerical modeling). ANd the Jain paper (DTIC), which deals
with multiple sines. I hadn't run across the one by Greenhall (who still
works at JPL)...
Thanks a bunch to the nuts..
Actually, if you think of it... for you to be able to even consider a
"waveform" you will need to do filtering, but then... the shape of that
filter will also have great influence on the overtone spectra... ruling
out analytic expressions. Noise degradation of hard limiter is analyzed
before, See chapter 6.5 Limiters in Gardner.
What are you *really* trying to achieve? 1-bit ADC at the end of a noisy
channel?
Cheers,
Magnus
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