Aliasing

Fourier Analysis · Axiom Academy

LESSON Aliasing: Undersampling Effects Understanding what happens when we sample below the Nyquist rate Aliasing occurs when a high-frequency signal is sampled too slowly, causing it to appear as a different (lower) frequency in the sampled data. The high-frequency signal takes on a false identity or "alias" - hence the name. 2. Why It Happens: Spectral Overlap When we sample at rate f s , the spectrum of the sampled signal repeats every f s Hz. If the original signal contains frequencies above f s /2 (the Nyquist frequency), these repetitions overlap, causing different frequencies to become indistinguishable. The condition for avoiding aliasing is the Nyquist-Shannon sampling theorem : the sampling rate must be greater than twice the highest frequency component in the signal. 3. Visual Examples: Wagon Wheel Effect Aliasing appears in everyday life! The classic example is the wagon wheel effect in movies: a wheel spinning forward can appear to spin backward or stand still. This happens because the camera samples at 24 frames/second, undersampling the wheel's rotation. Another example is moire patterns - when you photograph a fine pattern (like a screen or fabric), the camera's sensor undersamples it, creating artificial interference patterns. 4. Prevention: Anti-Aliasing Filters

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