Aliasing frequency calculator

This aliasing frequency calculator takes the true signal frequency and the sampling rate in hertz, applies the deterministic fold f_alias equals the absolute distance from the tone to the nearest multiple of the sampling rate, and returns the baseband alias in the closed interval from zero to the Nyquist frequency. It also reports whether the tone sits above Nyquist, which half-band Nyquist zone it occupies, and whether that zone inverts local spectrum order.

What aliasing is and how the principal alias is computed

The unique representative inside zero to Nyquist is therefore the distance from f to the nearest multiple of fs: f_alias equals the absolute value of f minus fs times the nearest integer to f over fs. That quantity is always between zero and the Nyquist frequency inclusive. When f is already at or below Nyquist, the nearest multiple is zero (or the tone itself sits on a half-bin edge) and f_alias equals f, so is_aliased is false whenever the signal frequency does not exceed Nyquist. This endpoint reports that zone as a one-based integer from the half-band index of f, plus a boolean spectrum_inverted flag for even zones, so you can reason about image polarity without recomputing band edges yourself.

Input contract, response fields, and invalid cases

POST a JSON body with two required finite numbers: signal_frequency, the true continuous-time tone in hertz, which must be non-negative; and sampling_rate, the sample clock in hertz, which must be strictly positive. Either field may arrive as a JSON number or as a numeric string; common aliases such as f, f_signal, frequency, fs, and sample_rate are accepted for convenience. Missing fields, empty strings, non-finite values, a negative signal frequency, or a zero or negative sampling rate fail with invalid_input and are not billed. On success the body echoes the rounded signal_frequency and sampling_rate, returns nyquist_frequency as half the sampling rate, aliased_frequency as the principal fold into zero to Nyquist, is_aliased true only when the signal frequency strictly exceeds Nyquist, nyquist_zone as the one-based half-band index, spectrum_inverted true on even zones, a short formula string restating the fold, and unit set to Hz. Example: signal_frequency one thousand and sampling_rate eight hundred yield nyquist_frequency four hundred, aliased_frequency two hundred, is_aliased true, nyquist_zone three, and spectrum_inverted false. The calculator does not perform anti-alias filter design, does not return full FFT bins, and does not simulate quantization noise; it answers the single closed-form sampling-theorem question of where a pure tone appears after ideal uniform sampling.

Where an aliased-frequency API earns its keep

Audio and music-technology curricula walk students through folding so they understand why a ten kilohertz whistle can look like six kilohertz when someone mistakenly samples at sixteen kilohertz; a deterministic oracle removes arithmetic slips from the lesson. RF and software-defined radio notebooks that practice intentional undersampling need the zone number and inversion flag when mapping intermediate-frequency plans onto the first Nyquist zone. Failed validation does not consume balance. Embedded and instrumentation teams use an aliasing frequency calculator when a scope, data logger, or cheap ADC shows a tone that does not match the known analog stimulus: feeding the known analog frequency and the configured sample rate returns the digital frequency that should appear if the front-end anti-alias filter leaked. Content sites that rank for aliasing frequency calculator or Nyquist foldback benefit from a live free browser path that matches the prepaid automation path on the same pure module. Keep requests small, pin the rounded fields in tests, and you get reproducible aliases for lab scripts, LMS plugins, and edge workers without standing up a full DSP stack of your own.