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In order to fully understand Nyquist's Theorem, one needs to understand the basics of waves and signals. The frequency of a wave is the rate at which waves are observed; that is, it is the number of complete oscillations of the wave per second. The period of a wave is the inverse of the frequency: it is the number of seconds required for one complete oscillation. The frequency of a wave is measured in Hertz, which is defined as 1/seconds, or cycles per second. The period is thus measured in seconds, sometimes phrased as seconds per cycle.<br /> | In order to fully understand Nyquist's Theorem, one needs to understand the basics of waves and signals. The frequency of a wave is the rate at which waves are observed; that is, it is the number of complete oscillations of the wave per second. The period of a wave is the inverse of the frequency: it is the number of seconds required for one complete oscillation. The frequency of a wave is measured in Hertz, which is defined as 1/seconds, or cycles per second. The period is thus measured in seconds, sometimes phrased as seconds per cycle.<br /> | ||
| − | + | Nyquist's Theorem states that if a signal contains no frequencies higher than a certain value ''B'', then the all of the necessary information in the signal can be captured with a sampling frequency of 2''B'' or higher. [5] This means that to obtain an accurate "picture" of a signal, the sampling period must be at most half the length of the period of oscillation of the signal. But why is this the case?<br /> | |
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Revision as of 08:46, 6 December 2020
Definition of Nyquist’s Theorem
In order to fully understand Nyquist's Theorem, one needs to understand the basics of waves and signals. The frequency of a wave is the rate at which waves are observed; that is, it is the number of complete oscillations of the wave per second. The period of a wave is the inverse of the frequency: it is the number of seconds required for one complete oscillation. The frequency of a wave is measured in Hertz, which is defined as 1/seconds, or cycles per second. The period is thus measured in seconds, sometimes phrased as seconds per cycle.
Nyquist's Theorem states that if a signal contains no frequencies higher than a certain value B, then the all of the necessary information in the signal can be captured with a sampling frequency of 2B or higher. [5] This means that to obtain an accurate "picture" of a signal, the sampling period must be at most half the length of the period of oscillation of the signal. But why is this the case?
