[From Bill Powers (930419.1530 MDT)]
The power of belief to create evil is burning up in Waco, Texas.
There must be a better way.
···
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Dan Miller (930419.1300)--
I tried to send you a direct post, and your address
miller@dayton.bitnet
didn't work. Undeliverable message.
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Martin Taylor (930419.1430) --
Could you tell me the bandpass shape or the impulse response of
the PIF
sp amplifier qc 0.0 1.0 1.0 # input function, 1-sec t.c.
This is like a linear amplifier with a single RC frequency
rolloff. The output will be flat from 0 to some frequency (rather
low) and then will make a transition to a 3db per octave rolloff
(I speak in voltage db; that's 6 db per octave in power).
I have done a Fourier analysis of your disturbance, and it is
very very far from a 1 Hz white noise.
I can't yet generate white noise, and filtering it to produce a
rectangular 1-Hz bandwidth would require an umpty-ump stage
filter to approximate the abrupt cutoff. Simcon does not yet have
a random number generator (that's coming soon). The disturbance
was generated as a series of three overlapping rectangular
pulses, and passed through exactly the same filter as used for
the input function, to create the net disturbance that you saw.
I have send you some fourier analyses showing that the spectrum
for the disturbance is exactly the same as the spectrum of the
perceptual signal, except for the amplitude scale.
... there is some problem about the filter bandwidth or its
physical realizability. A physical filter of 1 Hz bandwidth
cannot pass a signal with a delay of only 0.01 seconds.
A 1-Hz bandwidth produced the way I did it has a frequency
response that is 70.7 percent of the DC response at 1 Hz. It is
about 50 percent a 2 Hz, 25 percent at 4 Hz, and so on. The delay
of 0.01 sec that I mentioned is simply the transport lag -- 1
iteration of the program. That is not the same as the phase shift
of a sinusoid going through the filter. The phase shift is the
normal one you'd expect, 45 degrees at the frequency where the
amplitude response is down to 70.7 percent.
When I said this setup meets your requirements, I assumed (from
your previous posts) that you would be able to figure out the
equivalent rectangular bandwidth. The square waves going into the
disturbance filter have high-frequency components, so the
disturbance bandwidth has the same characteristics as the input
function bandwidth and contains many higher-frequency harmonics.
The driving waveform shouldn't make any difference, should it?
The disturbance should be generated by an impulse chosen from a
Gaussian random distribution every 1/2 sec and resampled with a
sinx/x filter for de-aliasing to exactly 1 Hz (but other
filtering schemes are OK, since sinx/x is non-physical. You
can't actually achieve a physical rectangular bandwidth for a
real signal).
Well, I don't know how to do that right off the bat. If you could
generate an ASCII file of values of the disturbance and send it
to me, I will soon be able to read it into Simcon one value per
iteration and use it in the simulation. I need at least an even
power of two values -- i.e., 1024, 2048 etc.
If it were not for the signal dynamics of the loop, which has a
fixed frequency-phase relationship, a simple sinusoid at 1 Hz
would be an adequate test disturbance, if the PIF were a clean
passband of 0-1Hz. But this won't do, because the phase
relation is very sensitive under such conditions. So we must
use a sharpish but realizable filter for the PIF, and a
disturbance with sufficient energy in the region of 1 Hz to
cover at least one cycle of phase lag.
You're right about the phase relationship being very sensitive.
If you make the rolloff in the PIF faster than 3 db per octave
(voltage), the phase will shift faster than the amplitude drops
off and you will turn the control system into an oscillator for
any loop gain greater than 1. The sharper you make the cutoff of
the 1-Hz response of the PIF, the worse this problem will be.
This is quite independent of whether you apply any disturbance or
not. The only feasible shape for the PIF bandpass is a 3 db per
octave rolloff, if you want a stable control system. If you try
to make the rolloff faster than that, you won't have a control
system.
If you send me your disturance tables I will plug them into the
model. But don't bother trying to formulate a sharp-cutoff filter
for the PIF: that's one of the cases where a rectangular
bandwidth is definitely NOT functionally equivalent to the real
bandwidth shape. It may be more convenient for computations, but
it ain't convenient for building a control system. Can't you work
with the actual bandwidth form and convert it to an equivalent
rectangular bandwidth? If you can't, you're going to have a hard
time finding any real systems to test against your hypothesis.
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Gary Cziko (930419.2041 GMT) --
I agree that when subjects are engaging in "good" perceptual
control that the independent variabe-dependent variable (IV-DV)
approach to research is problematic. But I wonder about
research in which reorganization (i.e.,learning, development)
is of main concern.
The best way to study reorganization is to measure the parameters
of control before and after (and maybe during). You have to have
an accurate model of behavior before you can say anything about
what has changed. All the IV-DV measures of learning I have seen
are so crude that you have no idea what actually changed inside
the organism. All you know is that the person or organism got
better at doing a task. What that implies about changes in
organization is unknown.
Consider a child acquiring language. It doesn't surprise me
that a child in the U.S. will learn English while one in
Mexico will learn Spanish. They may be both controlling for
the same types of variables, but in one environment one
language is effective while in another setting another
language must be used. There may also be more subtle
differences which could have effects on reorganization, such
as how easy it is to get mom's attention, whether there are
other siblings to compete with , etc.
If this is the kind of information you want, IV-DV is the way to
go. What external conditions correlate with changes in language
behavior? Once you know what conditions facilitate language
learning, all you have to do is set them up again, and all the
students will learn the language toot sweet, right?
If you want to know WHY those conditions make any difference, you
need to develop a model.
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Best,
Bill P.