Filter basics: anti-aliasing - AN928

In a sampled data system, frequency components greater than half the sampling rate "alias" (shift) into the frequency band of interest. Most of the time, aliasing in an undesirable side effect, so the "undersampled" higher frequencies are simply filtered out before the A/D stage. But sometimes, the undersampling is deliberate and the aliasing causes the A/D system to function as a mixer. This application note discusses the different filtering requirements for a sampled data system. It describes aliasing and the types of filters that can be used for anti-aliasing. Filtering is such a common process that we often take it for granted. When we make a cell phone call, the receiver filters out all other channels so we only receive our unique channel. When we adjust the equalizer on a stereo system, we are selectively increasing or decreasing the audio signal in a particular frequency band, using a bandpass filter. Filters play a key role in virtually all sampled data systems. Most A/D converters (ADCs) are preceded by a filter which removes frequency components that are beyond the ADC's range. Some ADCs have filtering inherent in their topology. Let's take a look at a sampled data system, the filtering requirements, and the relationship to aliasing. Background The maximum frequency component a sampled data system can accurately handle is its Nyquist limit. The sample rate must be greater than or equal to two times the highest frequency component in the input signal. When this rule is violated, unwanted or undesirable signals appear in the frequency band of interest. This is called "aliasing." For example, to digitize a 1kHz signal, a minimum sampling frequency of 2kHz is required. In actual practice, sampling is usually higher to provide some margin and make the filtering requirements less critical. To help understand a sampled data system and aliasing, we look at a classic cinematography example. In old western movies, as a wagon accelerates, the wheel picks up speed as expected, and then the wheel seems to slow, then stop. As the wagon further accelerates, the wheel appears to turn backwards! In reality, we know the wheel hasn't reversed because the rest of the movie action is still taking place. What causes this phenomenon? The answer is that the frame rate is not high enough to accurately capture the spinning of the wheel. To help understand this, suppose a visible mark is placed on a wagon wheel and the wheel is spun. We then take snapshots in time (or samples). Since a movie camera captures motion by taking a certain number of snapshots per second, it is inherently a sampled data system. Just as the film takes discrete images of the wheel, an ADC takes a sequence of snapshots of a moving electrical signal. When the wagon is first accelerating, the sample rate (the frame rate of the movie camera) is much higher than the revolution rate of the wheel, so the Nyquist criterion is met. The camera's sample rate is greater than twice the rate of revolution of the wheel, so it can accurately portray the wheel's motion and we see the wheel accelerating as expected (Figures 1a and 1b). At the Nyquist limit, we see two points that are 180 degrees apart (Figure 1c). These two points typically are indistinguishable from each other in time by the human eye. They appear simultaneous and the wheel appears to stop. At this wheel speed, the rate of the rotation is known (based on the sample rate), but the direction of the spin cannot be ascertained. As the wagon continues to accelerate, the Nyquist criterion is no longer met, and there are two possible ways to view the wheel. We can "see" it as spinning forward and the other spinning in the reverse direction (Figure 1d).