Resolution is not accuracy
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Resolution is not the same as accuracy: That was one of our favorite lessons from last week's Embedded Systems Conference in Boston.
Systems architect Kim Fowler made this distinction during his talk on analog-to-digital converters (ADCs), though its validity could apply to any process of digitizing real-world signals.
The distinction between resolution and accuracy is an important one insofar as while both reveal how well your digital processing system is measuring what it is supposed to be measuring, each describes an entirely different way in which you could get incorrect results.
"Resolution is the minimum span [the ADC] can measure," Fowler told attendees. "Accuracy speaks to how far the real transfer function of the ADC is from the theoretical transfer function."
Resolution is the smallest increment of input that a system would register as an event. It represents size as a single code value.
When thinking about resolution, picking the right sampling rate is critical. The sampling rate is the number of discrete samples taken per second, that are being taken of some continuous signal.
Sample at too low of a rate and you miss the critical contours of what you are trying to measure. Events could happen below detection levels, or your device could capture the beginning, but not the end of some event. Or vice versa.
Also, a low sampling rate can cause aliasing, when shadows of the thing being measured can muddy the image. Filters can be used, but different filters remove aliases in different ways, some of which might affect the results if you don't plan accordingly.
Engineers have long held that to accurately reproduce a signal, the sampling rate should be twice that of the highest frequency of what is being sampled. For instance, most digital recordings for audio CDs are sampled at 44,100 Hz, about twice that of the audible range for humans, which is about 20 Hz.
"That is an absolute minimum," Fowler said of this sampling rule-of-thumb, called the Nyquist'Shannon Sampling Theorem. "And if we are designing appropriately, we want to use that as a bottom line, but we want to have an appropriate margin above that."
For the most accurate signal reproduction, Fowler recommends a sampling rate of 5 to 10 times the original frequency.
Upping the resolution, of course, will provide a more complete picture of what you are trying to capture. But the higher sampling rate you want, the more you will pay for circuitry.
Even if you work out the best sampling rate for your budget, you still have to factor in accuracy issues.
Accuracy is the degree to which your measurement equals the thing actually being measured. The accuracy of ADC could be thrown off by several factors.
One factor, for instance, might be the quality of the ADC unit itself. "Fabrication of the ADC will inject harmonics into your signal," Fowler said.
Such harmonics can cause a nonlinear transfer function, meaning that the device captures input more accurately at some ranges than it does at others.
All of which goes along way to stating that incorporating a 24-bit ADC into your system design will not get you 24-bit fidelity. This worth keeping in mind when considering purchasing or building any system that has to convert some signal into digital form.
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