Translations:The Nyquist frequency/12/en

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According to our definition, is the sampling interval. The reciprocal of , namely , is the sampling frequency (or, equivalently, the sampling rate). For example, if , then the sampling frequency is samples/s. The sampling angular frequency is radians per second. Thus, we always must subtract some integer multiple of the sampling angular frequency to bring an actual angular frequency within the Nyquist range. The sampling frequency is one sample per , that is, . Thus, we see that the Nyquist frequency is one-half the sampling frequency. In the case when , the Nyquist frequency is , and the sampling frequency is . If a frequency f is outside the Nyquist range, its alias is found by subtracting from f an integral multiple of the sampling frequency; that is, the aliased frequency is , where k is the integer that makes the aliased frequency lie in the Nyquist range.