Nyquist sampling condition for band-limited signals

Sampling creates periodic spectral replicas. If fs is not greater than twice the signal bandwidth, replicas overlap and different inputs can produce the same sample sequence. The strict condition permits ideal reconstruction of a band-limited signal. Assume a band-limited signal and apply analog anti-alias filtering; practical sampling needs margin. Application: Set sampling rates and anti-alias limits for measurement and digital systems. The numerical example For a signal band-limited to 5 kHz, fs must exceed 10 kHz; 12 kHz meets the ideal condition if adequately filtered first anchors the idea in a concrete measurement case.

The Nyquist frequency is fs/2. It is the upper unique frequency limit of the ideal discrete spectrum at a given sampling rate, not the sampling rate itself. Real filters and measurement noise reduce usable bandwidth below it. Assume a band-limited signal and apply analog anti-alias filtering; practical sampling needs margin. The corresponding units are fs, fmax and fN in Hz. For a signal band-limited to 5 kHz, fs must exceed 10 kHz; 12 kHz meets the ideal condition if adequately filtered first. This checks that the reference quantities are compatible.

Ideal theory uses a sampling rate strictly above 2fmax; exactly at the boundary reconstruction is fragile, and a sinusoid at Nyquist loses phase information. Practical systems use margin and limit input bandwidth with an analog filter before conversion. Assume a band-limited signal and apply analog anti-alias filtering; practical sampling needs margin. Scope: The sampling theorem assumes a strictly band-limited continuous signal and ideal reconstruction. Practical systems need an analog anti-alias filter and margin above the theoretical boundary; Nyquist frequency is half the sampling rate, not automatically the highest reliably measured frequency with real filters. Undersampling makes frequency components appear as aliases. A practical application is Set sampling rates and anti-alias limits for measurement and digital systems.

Write the quantity and unit from the variable list next to every value: fs, fmax and fN in Hz. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For a signal band-limited to 5 kHz, fs must exceed 10 kHz; 12 kHz meets the ideal condition if adequately filtered first. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Assume a band-limited signal and apply analog anti-alias filtering; practical sampling needs margin.

The background states this starting condition: The sampling theorem assumes a strictly band-limited continuous signal and ideal reconstruction. Practical systems need an analog anti-alias. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Assume a band-limited signal and apply analog anti-alias filtering; practical sampling needs margin.