Nyquist Rate

Fourier Analysis · Axiom Academy

LESSON Nyquist Rate: Critical Frequencies in Sampling Understanding the minimum sampling rate for perfect signal reconstruction 1. The Nyquist Rate: Minimum Sampling Rate The Nyquist rate is the minimum sampling rate required to perfectly reconstruct a signal without information loss. For a signal with maximum frequency component f max , the Nyquist rate is: This fundamental theorem states that we must sample at at least twice the highest frequency present in the signal. Sampling slower than this rate leads to aliasing, where high-frequency components masquerade as lower frequencies. 2. The Nyquist Frequency: Maximum Representable Frequency The Nyquist frequency is the highest frequency that can be accurately represented at a given sampling rate f s : This is exactly half the sampling rate. Any frequency components above the Nyquist frequency cannot be distinguished from their lower-frequency aliases. The Nyquist frequency defines the bandwidth limit of a digital system. 3. The Relationship Between Nyquist Rate and Frequency These two concepts are complementary views of the same fundamental limit: From the signal's perspective: Nyquist rate = 2 f max tells us the minimum sampling rate needed. From the system's perspective: Nyquist frequency = f s /2 tells us the maximum frequency we can handle.

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