Voltages from items such as batteries, photovoltaic panels, and temperature sensors vary slightly and slowly over time, and for them, an added noise filter serves no purpose. On the other hand, signals that include unwanted components at frequencies above those you want to measure require a low-pass anti-alias filter to prevent unwanted high-frequency signals from “folding,” or aliasing, into your samples. The Nyquist-Shannon sampling theorem explains how and where such aliasing occurs based on a given sampling frequency.
Before you can choose such a filter, you must know the upper frequency (fc) of the signals you want to measure. Let’s set the fc value at 1,500Hz. You also must know the dynamic range of your analog-to-digital converter (ADC). Assume you have a 14-bit ADC, which provides a dynamic range of one part in 16,384, or about 84dB. That means the ADC will produce a result for any signal within that range, based on the full-scale input of the ADC.
Superimposed Butterworth-filter plots for fc values of 1,500Hz
and 2,000Hz show the frequencies at which 84dB attenuation
occurs. This value helps you determine sample rates for a
14-bit ADC.
An ideal anti-alias filter would completely remove all signals above the fc value -- 1,500Hz, in this case. But real filters attenuate signals at defined rates that vary by filter type. A two-pole low-pass Butterworth filter, for example, slowly attenuates frequencies and only reaches -84dB at 19kHz, so the ADC data would include many unwanted frequency components. An eight-pole Butterworth filter reaches -84dB at about 5kHz. So you would see less data from the ADC for higher-frequency components.
Filter specifications place the fc value at the -3dB point on a filter’s frequency versus attenuation curve, so needed signals at 1,500Hz would experience about a 30 percent reduction in amplitude. To avoid this unwanted attenuation, increase the fc value for the filter so signals at 1,500Hz have no attenuation. For the eight-pole Butterworth filter, an fc of 2,000Hz increases the frequency at -84dB to 6,700Hz. So the ADC can now measure signals up to this frequency.
What sample rate should you use for the ADC? The Nyquist-Shannon theorem explains the need to sample faster than twice the highest frequency. In this example, that component corresponds to the -84dB point on the filter response curve, or 6,700Hz, so you might think sampling at, say, slightly above 13.4ksamples/sec would do the job. But most measurement experts recommend from five to 10 times this upper frequency, so sampling from 33.5 to 67ksamples/sec provides better results. That means you sample at a rate from about 22 to 44 times higher than the 1,500kHz limit on your signals of interest.
If you would like to experiment with filter attenuation plots, schematic diagrams, and SPICE models, I recommend the free FilterLab software from Microchip Technology.
The next column explains the math (with a few equations) behind the frequency aliasing. Engineers often understand the concept of aliasing, but the math provides details.
We use them a lot in vibration testing/measurement. If you consider the sampling rate of a sine wave, and the apparent measured frequency of high frequency signals measured too slowly, Nyquist is a good place to start, but we typically acquire data at much higher speeds than 2X our filter cutoff frequency.
Execellent explanation on using filters and the Nyquist-Shannon theorem . This will be of great use to every engineer as Nyquist-Shannon theorem was and is realy the backbone of communication engineering. Thanks Jon!
Very nice explanation on using filters and the Nyquist-Shannon theorem - something every test engineer needs to keep in mind when determining their sampling rate. Thanks for another great article, Jon!
I recommend using an anti-alias filter whenever you must measure anuthing more than a DC, or near-DC signal. Some companies include them in data-acquisition equipment or on analog-to-digital-converter (ADC) boards, and some don't, so it pays to ask. If a board or system includes a filter or filters, find out how much control you have over it and get a plot of frequency vs. attenuation (a Bode plot) and a plot that shows phase vs. frequency. I didn't get into phase changes in this column, but people should know that filters change phase relationships of signals, too. Those changes could affect measurements when you must correlate signals in the time domain.
Engineers can build their own anti-alias filters, but I don't recommend that course unless they have filter-design experience and plan to build a lot of them. Commercial filters are the way to go in almost all situations.
Interesting article, Jon. Are these filters widely used these days? And who is using them? Is this mostly for large, advanced organizations or is it more more widely deployed?
The Machinist Calc Pro computes speeds and feed rates for milling, turning, and drilling: cutting speed, spindle speed, feed rate (inches/minute), cutting feed, etc.
During a recent meeting with engineering-school faculty and alumni, Contributing Technical Editor Jon Titus talked about whether colleges should educate generalists or specialists. What do you think?
From Dell / Intel® New Paradigms in Design Work Scott Hamilton, vertical market strategist for Dell Precision workstations, 5/2/2013 3
Early in my career, I worked as a draftsman and remember the days of drawing on vellum with numbered pencils and Mylar with plastic lead. This was a fun experience in the sense that I ...
I've been using workstations for more than 10 years and love finding ways to get more performance from my system. With demanding professional applications that require more power each ...
A lasting memory from my first job as an engineer in an auto assembly plant is standing on hard concrete at six in the morning, vending-machine coffee clutched in hand, listening to ...
A quick look into the merger of two powerhouse 3D printing OEMs and the new leader in rapid prototyping solutions, Stratasys. The industrial revolution is now led by 3D printing and engineers are given the opportunity to fully maximize their design capabilities, reduce their time-to-market and functionally test prototypes cheaper, faster and easier. Bruce Bradshaw, Director of Marketing in North America, will explore the large product offering and variety of materials that will help CAD designers articulate their product design with actual, physical prototypes. This broadcast will dive deep into technical information including application specific stories from real world customers and their experiences with 3D printing. 3D Printing is
To save this item to your list of favorite Design News content so you can find it later in your Profile page, click the "Save It" button next to the item.
If you found this interesting or useful, please use the links to the services below to share it with other readers. You will need a free account with each service to share an item via that service.
Tweet This
2 
