This is probably a good example of Guido's observation about the
readability of reduce on non-associative arguments: almost always, an
explicit loop would be easier to read.
My bad.
I think this is the kind of PLL that Massalin, around p.99 of her
dissertation, calls a "FLL", for "frequency-locked loop".
Definitely failed to communicate then. It tracks the difference
between leading edges of the local oscillator and the signal, so even
with matched frequencies, the phase difference gets integrated. (if
the frequencies differ enough that there are multiple leading edges
for each lagging, then they should sum linearly so the feedback
signal is even stronger)
If I understand properly, the dot product style of phase detector has
a region where it produces the wrong sign for a stable lock, whereas
this detection will lock properly for all phase differences.
-Dave
# odelta: calculate the adjustment by comparing lead/lag of cycle
starts
# oprime: scan-update the local oscillator value
odelta = lambda osc, sig: compare(wav(osc),wav(sig))/4096.0
This looks like a bit of cheating --- for every "sample", you
generate a
whole new signal as if that oscillation were continued for 1024
samples?
Maybe I didn't understand.
That was an artifact of my tracing output; I was trying to simulate a
signal that changed relatively slowly (sig is not the sample, the
1024 elements of wav(sig) are), and because I'm not sure how to
express an actual FM signal (product of sines?), it's doing step-
function frequency changes. (might be interesting to try with just
phase, to see how well this would track phase-shift keying?)
zeroph = lambda w: [(i<0 and j>0) for i,j in zip(w[:-1],w[1:])]
I wonder, would this work
better with (i<0 and j>=0)? With < and > it ought to miss the
zero-crossing occasionally.
True, but in general it's not very robust; you'd probably want to
loosen the logic, and look for something that went from significantly
below zero to significantly above within a small number of samples,
rather than tightening it.
The page I found about LIAs makes them sound like they're just
what I'm doing in the longer C pitch-detection program: taking a
low-pass-filtered "dot product" between the input and a second
90°-offset waveform generated by the oscillator.
The cool thing about LIAs is that they introduce an artificial
switching into a signal (the example H&H gives is a telescope that
physically switches the mirror back and forth from the subject to a
control). This way, stuff that correlates well with the switched
condition is highly likely to be signal, and instrument noise will
likely be the same no matter which way the switch is pointing. (and
1/f noise should be lower at a high f than at dc) Maybe I haven't
understood what you're describing, but it sounds to me more like AM
demodulation via PLL.
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