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Analog to digital: Frequency

August 20, 2010

Dear Control Engineering: I was looking at the discussion about bit rate, but can you go into more depth on how frequency works in this context?

If bit rate is the vertical or y-axis on our graph, frequency is the horizontal or x-axis. Bit rate says how many divisions you have on y, and frequency says how often you make a mark. Here’s an analogy. Say you need to draw a series of parallel lines 1/8 in. apart. If you have a ruler and a pencil with a sharp point, that’s no problem. But if all you have is a chisel point marker that makes a thick line 1/4 in. wide, you will have a hard time. Your drawing instrument has to be finer than the distance between the lines.

It’s the same when converting analog data to digital. Just as you must have a sufficient bit rate to duplicate subtleties in the analog waveform, your frequency also has to be up to the task. The rule of thumb is that the digital frequency has to be at least double the highest analog frequency that you have to convert. Last week we noted that audio CDs have a frequency of 44.1 kHz. Why that number? It’s because audio engineers wanted to be able to create sounds with frequencies as high as about 20 kHz. Using 44.1 kHz gave them better than double. The audio on a DVD is 48 kHz which gives even more latitude.

If you want to apply this in an industrial control context, you system has to have the same capability. If you read our article Solving Process Instability, we made the point that a control system has to have a faster response time than what it is trying to control. Let’s say some element of your process tends to oscillate and you see the waves are one minute apart. You want your control system to compensate for that. If your system's respose is slower than that frequency, it will always be behind what it is trying to fix. Your system has to be able to respond even faster than the problem if you want any hope of flattening the line.

Peter Welander, pwelander(at)
Control Engineeing

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