![]() Note that as the maximum signal frequency approaches the Nyquist frequency, the total number of samples needed to reconstruct the signal accurately approaches infinity.Īliasing is a fundamental mathematical result of the sampling process. The process seems to indicate that the original signal was a 100 Hz sine wave, the difference between the actual input wave and sampling frequencies. As an example, Figure 1 shows the result of sampling a 900 Hz signal at 1 kHz. Frequencies above Nyquist appear as false low-frequency aliases. No practical data-acquisition system can sample fast enough to catch all of a real signal's components. To correct the image in the movie example, the frame rate would have to exceed twice the rotation speed of the wheel (or its spokes) or of the helicopter blades. This erroneous image, known as an "alias", occurs because a "motion picture" camera actually samples continuous action into a series of stills, and the frame rate (commonly 24 or 30 frames per second) is not fast enough or is nearly an exact multiple of the object's rotation speed.Īccording to Nyquist's Theorem, accurately representing an analog signal with samples requires that the original signal's highest frequency component be less than the Nyquist frequency, which is at least half the sampling frequency. A graphic example is the movie scene that apparently shows wagon wheels or helicopter blades turning backwards. The digital version of a signal may not resemble the original in some important respects. Unfortunately, sampling often sacrifices accuracy for the sake of convenience. Many data-acquisition systems must also construct a representation of the original signal from the digital data stream. ![]() The converted digital data may then be manipulated mathematically. Operating on these signals efficiently often requires the filtering, sampling and digitizing of the analog data using A/D converters. Most physical (real world) signals are analog.
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