The Math of Digital Audio – Sampling and Aliasing

Analog audio is converted to digital by sampling at regular intervals. The Nyquist–Shannon sampling theorem says: to avoid aliasing, sample at more than twice the highest frequency. Human hearing goes up to 20 kHz, so CD audio samples at 44.1 kHz. Aliasing occurs when high frequencies ‘fold’ into lower frequencies, creating false tones. Reconstruction uses a low‑pass filter (mathematically a sinc function convolution). The same mathematics applies to digital images (pixels), medical imaging (MRI), and wireless communications.