what is foldback aliasing in audio sampling?

Explaining foldback aliasing

Foldback aliasing is a DSP concept where frequencies above the Nyquist limit reflect back into the baseband due to spectral periodicity. This often occurs in synthesis, like with non-bandlimited waveforms such as sawtooth or square waves. To avoid it, use techniques like anti-aliasing filters or oversampling. The alias frequency is calculated by the formula: $f_{\text{alias}} = |k \times f_s \pm f|$.

Clarifying foldback aliasing

When a continuous frequency $f_0$ is sampled at $f_s$, the discrete aliasing frequency $f_a$ is given by $f_a = |f_0 - m \times f_s|$, where m ensures $f_a \leq f_s/2$. Foldback happens when analog signals above Nyquist reflect to lower frequencies, creating reversed images. For example, a 30kHz sine wave sampled at 44.1kHz folds to 14.1kHz.

Explaining aliasing in synthesis

In aliasing, frequencies above half the sampling rate fold back across multiples of the sampling rate. For example, a 30 kHz tone sampled at 44.1 kHz folds to 14.1 kHz. For a square wave at 1 kHz, any harmonic above 22.05 kHz will fold back. To compute the alias, use:
$f_a = |n \times 1k - m \times 44.1k|$ where $m$ is chosen so $f_a \leq 22.05k$.

Clarifying aliasing vs foldback aliasing

Aliasing occurs when frequencies above the Nyquist limit fold into the baseband. Foldback aliasing specifically refers to how these frequencies reflect back downward around the Nyquist point, creating reversed spectral content. To avoid this, use anti-aliasing filters, oversampling, and band

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