Filter Tutorial - Using Filters to Eliminate Sampling Errors in A/D Conversion Systems
Everyone who has gone to the movies has probably seen an example of aliasing. It's what the makes the spokes of a wagon wheel or the rotor blades of a helicopter appear to be rotating slowly backwards.
In data acquisition systems, aliasing is a sampling phenomenon that can cause gross errors in results and reduce the accuracy of the data collected by an A/D card, which converts the analog output of a sensor into a digital number that can be read by the acquisition system's computer. It occurs whenever an input signal has frequency components at or higher than half the sampling rate. If the signal is not correctly band limited to eliminate these frequencies, they will show up as aliases or spurious lower frequency errors that cannot be distinguished from valid sampled data. The alias signals are actually at a higher frequency, but are converted by the sampling process to a false frequency below half the sampling rate. For example, with a sampling rate of 1,000 Hz, a signal at 800 Hz will be aliased to 200 Hz (the false lower frequency). Thus, aliasing is a phenomenon that occurs when a high-frequency component effectively takes on the identity of a lower frequency.
Slight fluctuations in the measured environment or the measured signal can cause alias signals to move, leaving errors in different locations throughout your data each time you use an A/D converter.
One solution to the aliasing problem is to sample the signal at a very high rate and then filter out the high frequencies with digital techniques. But, such oversampling of data increases system costs by requiring faster A/D conversion for digital processing, more memory, and higher bandwidth buses. It also leads to higher analysis costs by creating more data to process and interpret.
A more practical alternative is to limit the bandwidth of the signal below one-half the sample rate with a low-pass or anti-alias filter, which can be implemented on each input channel in front of the A/D converter. Low-pass filtering must be done before the signal is sampled or multiplexed, since there is no way to retrieve the original signal once it has been digitized and aliased signals have been created.
To avoid aliasing with a low-pass filter, two processes actually must occur:
Under ideal conditions, a low-pass filter would exactly pass unchanged all slower signal components with frequencies from DC to the filter cutoff frequency. Faster components above that point would be totally eliminated, reducing the signal disturbance. But, real filters do not cut off sharply at an exact point. Instead, they gradually eliminate frequency components and exhibit a falloff or rolloff slope. These attenuation slopes typically range from 45 dB/octave to 120 dB/octave and "bottom out" at some finite value of stopband rejection, typically 75 to 100 dB.
A simple illustration of these processes can be seen in the case of the 800 Hz frequency aliasing to 200 Hz (see above). Suppose that the 800 Hz is an unwanted interfering signal caused by an unwanted mechanical vibration. To prevent its alias from causing significant data errors at 200 Hz, the 800 Hz frequency must be removed by a low-pass filter. If the cutoff point is set near 450 Hz, a filter with a steep rolloff slope will eliminate the 800 Hz frequency, making the false 200 Hz frequency disappear. The input frequencies of interest below the filter cutoff (450 Hz) will still pass through the system unchanged.
High-frequency components can result from the inherent noise of the system itself and from noise or interference not related to the DAS, including 50Hz or 60Hz pickup, broadcasting stations, and mechanical vibrations. High-frequency components also are inherent in any sharp transitions of the measured signal. Low-pass filters generally can eliminate alias errors produced by these sources as long as the filters precede the A/D converter.
The aliasing phenomenon becomes a problem in A/D conversion systems when an input signal contains frequency components above half the A/D sampling rate. These higher frequencies can "fold over" into the lower frequency spectrum and appear as erroneous signals that cannot be distinguished from valid sampled data. The best approach to eliminating false lower frequencies is to use a low-pass filter, which inhibits aliasing by limiting the input signal bandwidth to below half the sampling rate. A low-pass filter, which is applied to each input channel in front of the A/D card, also eliminates unwanted high-frequency noise and interference introduced prior to sampling. It reduces system cost, acquisition storage requirements, and analysis time by allowing for a lower sampling rate. Finally, a low-pass filter serves as an important element of any data acquisition system in which the accuracy of the acquired data is essential.
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