Frequencies above the Nyquist frequency fold back into the audio band as inharmonic aliases

Sampling can be viewed as modulating the audio signal with a pulse train at the sample rate, which creates copies of the spectrum around each multiple of the sample rate. If the signal contains any frequency above half the sample rate (the Nyquist frequency, sr/2), the lower sideband of a copy falls within the audio band, appearing as an alias tone: a frequency reflected back below Nyquist by fo = fc − N·sr, where N is the nearest integer to fc/sr. These aliases are unrelated to any real source frequency and typically inharmonic, sounding like metallic ringing; harmonically rich sources such as a sawtooth alias heavily because many of their partials exceed Nyquist. A key boundary condition: aliasing cannot be undone after sampling — the reflected component is mathematically indistinguishable from a genuine tone at that frequency, so filtering it also removes any legitimate content there. The fix is prevention: a lowpass anti-aliasing filter before the ADC (and a reconstruction filter after the DAC), or bandlimited/oversampled oscillators that keep content below Nyquist.

Examples

sr = 500 Hz, Nyquist = 250 Hz: a 300 Hz tone aliases to 200 Hz (500−300). sr = 44.1 kHz: a 46.2 kHz tone folds to 2.1 kHz. A 10 kHz sawtooth at sr = 48 kHz has a 30 kHz partial folding to 18 kHz. Pitching a wavetable up requires band-limiting; oversampling raises Nyquist before filtering.

Assessment

At sr = 22050 Hz a 15000 Hz component is generated: calculate its alias and explain why a lowpass filter applied after conversion cannot remove it. (Then: at sr = 44.1 kHz, where does a 25 kHz harmonic alias? Show your working.)