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Sample Rates Revisited

Jon Titus, Contributing Editor -- Design News, October 6, 2008

In my previous Tips column (Sept. 22), I noted my rule of thumb for sampling at five to 10 times a signal's bandwidth. That range provides a good starting point, but you can better determine a sample rate for given signal conditions. To start, assume you have a signal that includes unwanted harmonics, noise or other signals of no interest. To remove these signals you use an anti-alias filter — usually a low-pass filter — so your analog-to-digital converter (ADC) “sees” only the signals of interest.

Unfortunately, you cannot make a “brick-wall” filter that, at a specific frequency, instantly goes from passing all signals to blocking all signals. Filters have a characteristic roll-off that attenuates signals at different rates. The roll-off varies by filter type and the number of filter stages or poles. A 2-pole low-pass Butterworth filter, for example, provides a shallow attenuation with frequency whereas an 8-pole Chebychev low-pass filter offers a steep attenuation. Filters also have a characteristic cut-off frequency (fc), specified as the point at which filter attenuation drops to and stays below -3 dB.

I'll use a 5-pole Butterworth filter as an example and you can see its response in the graph, above. This filter starts to roll off at about 650 Hz, the highest frequency component I want to examine in my unknown signal. This low-pass filter reduces the signal amplitude by half at 3 dB at 1 KHz and by 30 dB (1,000 fold) at 2 KHz.

Assume I plan to use a 16-bit ADC to digitize my signals. That converter has a dynamic range of 1 part in 65,536, or about 48 dB. Look at the filter graph and you'll find the -48 dB point at about 3,030 Hz. So, even though I use a filter to remove signals above 650 Hz, my ADC must digitize signals out to 3,030 Hz. As a result, I need to set the ADC to sample at more than 6,060 samples/sec or my digitized data will include aliased signals. So, even though I want to digitize a 650 Hz signal, with this filter configuration I must oversample at over about 10 times the frequency of the signal.

You can change filter characteristics to obtain a sharper attenuation. An 8-pole Butterworth filter with an fc equal to 880 Hz, for example, reaches the -48 dB point at 1,750 Hz. So you could sample at more than 3,500 samples/sec, or over five times the 650 Hz signal frequency. Both sample rates in these examples come close to my rule of thumb. If I had a higher-resolution ADC, my sample rate would have to increase. So, remember there's more to sampling than just the Nyquist criterion.

There are other reasons to oversample a signal and I'll cover them in another column. If you want to experiment with filter characteristics and anti-alias filters, I recommend the free FilterLab software from Microchip Technology.

This plot shows the frequency response of an 8-pole (blue) and a 5-pole (red) Butterworth anti-alias filter.

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• Sample rates revisited.Mr Titus.You got it all wrong!The dynamic range of a 16 bit converter is...
  Hans J Weedon - 2008-10-15 12:54:36

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