Wed, 22 Mar 2006

Synthetic Instruments are Not Slow

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:

"While we can achieve a number of different instrument/measurement capabilities in a compact format in SI, it comes at the cost of in general a much more significant software task for the end user or system integrator and generally a much longer time/measurement."

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.

So what about the speed of synthetic instruments? I claim they are the fastest possible instrument. Why do I say that?

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.

Posted Mar 22, 2006 at 00:35 UTC, 756 words,  [Permalink

Buy My Book!

Synthetic Instruments: Concepts and Applications

Contact Me

©2006 C.T. Nadovich, All Rights Reserved