Nyquist Rate & Aliasing
Check whether your sample rate clears Nyquist and find the alias frequency a tone folds down to.
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The engineering
The sampling theorem says a signal is fully recoverable only if the sample rate exceeds twice its highest frequency component. Half the sample rate is the Nyquist frequency; any energy above it folds back down into the baseband and masquerades as a lower tone you can never remove after the fact. This card tells you the fold-down frequency for a single tone and whether you're in trouble.
The classic gotcha: a clean-looking captured waveform is no proof you sampled fast enough — a 1.1 kHz tone sampled at 1 kHz looks exactly like 100 Hz. Always band-limit with an anti-alias filter before the ADC, and budget the sample rate for the highest real frequency present, not just the one you care about.
Where this math comes from
Harry Nyquist, a Bell Labs engineer working on telegraph transmission, published the bandwidth-versus-signaling-rate result in 1928 while trying to squeeze more channels onto telephone lines. Claude Shannon gave it the rigorous information-theory footing in his 1949 paper, framing it as the reconstruction condition for band-limited signals — which is why it's often called the Nyquist-Shannon sampling theorem.
Similar results were reached independently by E. T. Whittaker (1915), Vladimir Kotelnikov (1933) in the USSR, and others, so the theorem carries a small crowd of names depending on where you learned it. The modern DSP treatment engineers actually reach for is Oppenheim and Schafer's textbook, which formalizes aliasing as spectral folding about integer multiples of the sample rate.
- 1928Harry NyquistRelates signaling rate to bandwidth in telegraph transmission.
- 1933Vladimir KotelnikovStates the sampling theorem independently in the USSR.
- 1949Claude ShannonGives the reconstruction condition its information-theory proof.
- 1975Oppenheim & SchaferCodify aliasing as spectral folding in the standard DSP text.
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