Aliased Frequency Calculator

Aliasing was first documented in practical engineering by Harry Nyquist in his 1928 paper on telegraph transmission theory — he showed that reconstructing a signal from samples requires the sample rate to exceed twice the highest signal frequency. Claude Shannon\'s 1949 sampling theorem paper formalized the reconstruction condition and explicitly worked out the aliasing phenomenon for violations of the Nyquist condition.

The "wagon wheel" phenomenon in movies — wheels appearing to stand still or rotate backward — is the same physics as electronic aliasing. At 24 frames per second, rotations above 12 rev/s produce aliased perceived rotation. This visual example is how signal-processing instructors have explained aliasing to students for 70+ years.

Anti-alias filters became critical infrastructure as digital audio matured in the 1970s. Early CD players paired analog brick-wall anti-alias filters with 44.1 kHz sampling; modern audio ADCs use Σ-Δ oversampling with digital decimation, moving the sharp filter skirt from the analog domain (expensive, bulky) into DSP code (cheap, programmable). Intentional aliasing also found productive use: bandpass sampling in software-defined radio lets a properly-filtered high-frequency signal fold into baseband for easier digital processing.

Enter a sampling rate and an input frequency. The tool computes which Nyquist zone the input sits in, whether it falls inside the baseband or aliases, and if it aliases, where it appears in the 0 to f_s/2 band. Odd-zone inputs fold "straight" (same order); even-zone inputs fold "mirrored" (reversed order).

Useful for: diagnosing mystery spectral lines in digitized signals, designing bandpass-sampling receivers (picking f_s to land a target band in a useful alias position), and verifying that your anti-alias filter has adequate attenuation above the frequency at which aliased content would become a problem. All math runs client-side.