The Fundamental Limit of Digital Recording
In 1949, Claude Shannon proved that a continuous signal can be perfectly captured by discrete samples — but only if you sample fast enough. Specifically, the sampling rate must exceed twice the highest frequency in the signal. This elegant result underpins every digital system: CDs, digital cameras, MRI scanners, and seismographs all obey this one theorem.
When Sampling Goes Wrong: Aliasing
Sample too slowly and something strange happens — high frequencies masquerade as low frequencies. This is aliasing, and you have seen it in action: wagon wheels appearing to spin backwards in movies, or moiré patterns on striped shirts on television. The simulator above lets you watch aliasing emerge as you lower the sampling rate below the Nyquist limit.
Perfect Reconstruction
When the Nyquist criterion is satisfied, Shannon showed that sinc interpolation can reconstruct the original continuous signal exactly from its discrete samples. In practice, real systems use approximations (linear or polynomial interpolation), but the theoretical guarantee of perfect reconstruction is what makes digital audio sound identical to the analog original.
From Theory to Practice
CD audio uses 44,100 samples per second — just over twice the 20 kHz upper limit of human hearing. Telephone systems sample at 8,000 Hz for the 4 kHz voice band. Radar systems, medical imaging, and software-defined radio all choose their sampling rates based on Shannon's theorem. Getting it wrong means permanent, irrecoverable information loss.