On Fri, 20 Oct 2006 18:44:04 +0200, Dave Long wrote:
Are there other cases where people have used LFSR sequences rather
than counters?
I first ran into them for planetary missions. An LFSR has a -0
autocorrelation everywhere but within half-a-bit of synchronized, and
which point it ramps up to a huge autocorrelation when exactly
synchronized.
That's interesting. True of all LFSRs, or just maximal ones? And by
"-0" do you mean "roughly zero" (true of approximately all
pseudorandom sequences) or "exactly 0"?
Squeeze this witch hat enough (run a very long, very
fast sequence) and you get a nice spiky delta-function-like thing,
which means you can resolve small features with the return signal.
(it's the chipping version of what we were talking about with chirps)
_______________/\_______________/\_______________/\_______________/\
Also true if your signal is just an occasional square pulse --- but
that gives you much lower power and therefore lower noise immunity.
The time-domain radio folks are exploring the middle ground, where you
use a large number of pulses sparsely but randomly distributed.
I read a paper some years ago about image coregistration that got a
similar nice clean peak without the privilege of choosing the input
data, by FFTing the images, normalizing the magnitude of each
frequency to one, leaving just the phase information, and doing the
autocorrelation from the resulting radically sharpened image (in the
frequency domain). Doing the autocorrelation on a 1/f signal (like a
typical real-world image) gives you fairly flat peaks, since most of
the energy is in the low frequencies.
The paper called the technique "phase correlation".
(Maybe I should read up on Walsh transforms and wavelets, since if
they could be applied to that problem, it would be quicker or require
less silicon.)
This always seemed like a somewhat dubious technique to me, since
you're amplifying whatever noise frequencies exist in the original
image until they're as strong as the frequencies that carry signal.
Maybe it would work better if you zeroed the phasors for the
frequencies with energy far below 1/f.
(CDMA works because different codes won't interfere with each other as
long as they all control their gain well -- I don't know how that's
done, but maybe the side slopes on the correlation would allow a device
to make fine adjustments for how it's moving relative to the base?)
I'm not sure the path length is necessarily that strongly connected to
the signal attenuation; at least in the 2.4GHz spectrum I'm most
familiar with, things like concrete walls usually matter more.
(By the way, may I forward your response to kragen-discuss, or did you
send it privately on purpose?)
