For some reason, people have been taking exception to the fact that
synthetic instruments are the fastest possible instrument. I'm hearing
objections to this point from several different directions.
When I gave a talk recently at NI, there was some grumbling in the
audience when I showed a slide that claimed a speed advantage for SI.
Not long afterward, I pick up the March 2006 issue of Microwave
Journal and find in David Menzer's article a whole flock of
erroneous comments regarding synthetic instruments, including the
doubly fallacious statement:
I think both mistakes in this one sentence stem from a single problem
with the whole article: it doesn't quite commit to what a synthetic
instruments are. The article passively quotes the Wiki definition of
SI, and that is as close to the truth as it ever gets. The rest
of the article veers off into talking about other issues, like modular
mechanical packaging and digital bus standards, punctuated by a few
misleading comments like the one quoted above. Since Menzer is
clearly a smart and well educated man (he and I both went to RPI, so I
have to believe he's a good guy) I'm shocked that he would allow his
article to wander off-topic like it does.
I say it because synthetic instruments are abstract descriptions of a
measurement. They are software – an algorithm. As such, they can
describe any sort of verifiable and finite state measurement
process. In fact, I might also claim that the very essence of any
"measurement" is the defined process of estimating the numerical value
of a measurand.
You might argue that there are things in this world that can't be
measured by a finite, verifiable algorithmic process. Truth, beauty,
good, and evil may be some of them. I stand humbly corrected if the
objection to my claim of the supreme speed of a synthetic instruments
is based on such grounds: that these sorts of subjective measurements
aren't covered. But if, on the other hand, I can assume without loss
of generality that the set of measurements of interest to scientists
and engineers are those measurements describable by a finite,
objective, verifiable algorithm, then synthetic instruments can
measure them all.
Of all the possible algorithms for measuring a given thing, there is
always at least one algorithm that is not slower than any of the other
possibilities. Since a synthetic instrument can always be designed
that execute any of these "fastest" algorithms, my claim that a SI can
make the fastest possible measurement of a given measurand is proved
true.
Consider frequency measurement for an example. A common natural
instrument for measuring frequency is a counter. A counter has
mesurement specific hardware that measures frequency by counting
cycles over a certain time interval. For a fixed number of digits of
precision, this "natural instrument" algorithm is fast if the
frequency is high, or quite slow if the frequency is very low. In
contrast, a synthetic instrument can be designed that uses
any algorithm for measuring frequency. The SI that we run on
measurement agnostic hardware is not locked into a certain algorithm
in the same way it is when we just have a natural instrument. A SI can
count cycles, for sure, but alternatively it could use an eigenvector
based algorithm from modern spectral estimation to give a highly
precise frequency measurement in less than a single cycle of the
waveform. Speed wise, this would beat the pants off counting, or even
an FFT, especially when low frequencies are measured.
Of course, the question remains open if a particular hardware
measurement system can execute the "fastest" SI at its maximum
theoretical speed. It's always possible to take a fast algorithm and
run it slower. Thus, we could expect to find pathological examples of
a natural instrument using a sub-optimum algorithm on fast hardware
that measures something faster than a synthetic instrument with the
fastest algorithm running on slow hardware.
But so what? These are exceptions that prove the rule. The fast
algorithm will ultimately win in the end. And if we are talking about
synthetic instruments, the algorithm is everything. QED.
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