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Sampling and Nyquist

To digitize a signal correctly we must take enough samples per second. The Nyquist criterion says the sampling frequency must be more than twice the highest frequency component in the signal. If we sample too slowly, aliasing occurs: the signal appears as a completely different (lower) frequency after sampling, and this error cannot be corrected afterward.

f_s>2f_{max}

Nyquist criterion for correct sampling

Symbols

$f_s$	sampling frequency	Hz
$f_{max}$	highest frequency component in the signal	Hz

Example

Signal up to $1$ kHz:

Minimum theoretical sampling frequency: $f_s>2\cdot1=2$ kHz.

Filter out everything above

f_s/2

*before* sampling – aliasing cannot be removed afterward.

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Part of Embedded Systems and Instrumentation: Measurement.