Opening your learning space
Starting the app …
Opening your learning space
Starting the app …
A band-limited signal can be ideally reconstructed when the sampling frequency exceeds twice its highest frequency.
Free to browse · flashcards or a multiple-choice quiz · import from Essential
Formula
fs and fmax in Hz
| Symbol | Meaning | Unit |
|---|---|---|
| Sampling frequency | Hz | |
| fmax | Highest frequency present in the signal | Hz |
f_s>2f_{max}The sampling theorem assumes a strictly band-limited signal and ideal uniform sampling. Practical systems need anti-aliasing filters and margin because real filters do not have a perfect cutoff. Below the limit, spectral replicas overlap and higher frequencies appear as false lower-frequency components. Sampling exactly at the boundary is not a robust design for arbitrary phase.
The sampling theorem assumes a strictly band-limited signal and ideal uniform sampling. Practical systems need anti-aliasing filters and margin because real filters do not have a perfect cutoff. Below the limit, spectral replicas overlap and higher frequencies appear as false lower-frequency components. Sampling exactly at the boundary is not a robust design for arbitrary phase.
A band-limited signal can be ideally reconstructed when the sampling frequency exceeds twice its highest frequency.
Defining relation
The equation states the defining relation within its stated domain.
Use the example for Nyquist–Shannon sampling limit to explain which inputs determine the requested output.
The example connects concrete inputs to its result.
A band-limited signal can be ideally reconstructed when the sampling frequency exceeds twice its highest frequency.
The relation applies only under its stated assumptions.
Applying the relation to a different case without checking its stated assumptions.
Check the validity range before substituting values: The sampling theorem assumes a strictly band-limited signal and ideal uniform sampling. Practical systems need anti-aliasing filters and margin because real filters do not have a perfect cutoff. Below the.
Formula cluster
A band-limited signal can be ideally reconstructed when the sampling frequency exceeds twice its highest frequency.
If a signal contains frequencies up to 4 kHz, the ideal condition is fs>8 kHz; practical design uses a higher rate and an anti-aliasing filter.
Specify ADCs, audio, sensors, imaging and digital measurement chains.
Here is how to work through a typical Nyquist–Shannon sampling limit (Abtastfrequenz fs > 2 · maximale Signalfrequenz fmax) task step by step:
Task
Use the example for Nyquist–Shannon sampling limit to explain which inputs determine the requested output.
Solution path
The example connects concrete inputs to its result.
A band-limited signal can be ideally reconstructed when the sampling frequency exceeds twice its highest frequency.
The relation applies only under its stated assumptions.
The relation fs>2f_{max} summarizes A band-limited signal can be ideally reconstructed when the sampling frequency exceeds twice its highest frequency. Read it as a model for defined quantities, not as an automatic claim about every real situation. In the example If a signal contains frequencies up to 4 kHz, the ideal condition is fs>8 kHz; practical design uses a higher rate and an anti-aliasing filter., symbols are connected to concrete values and the result is interpreted in context. Validity limit: The sampling theorem assumes a strictly band-limited signal and ideal uniform sampling. Practical systems need anti-aliasing filters and margin because real filters do not have a perfect cutoff. Below the Source: MIT OpenCourseWare 6.003, Signals and Systems, sampling and reconstruction lecture materials.
First write down the requested quantity and all given values with their symbols. Substitute them into the defining relation and check unit consistency. The example If a signal contains frequencies up to 4 kHz, the ideal condition is fs>8 kHz; practical design uses a higher rate and an anti-aliasing filter. provides a worked check: formula and result must have compatible scale and meaning; round only at the end. Validity limit: The sampling theorem assumes a strictly band-limited signal and ideal uniform sampling. Practical systems need anti-aliasing filters and margin because real filters do not have a perfect cutoff. Below the Source: MIT OpenCourseWare 6.003, Signals and Systems, sampling and reconstruction lecture materials.
The formula applies only when quantities are defined as in the source and background. Check boundary cases, measurement conditions and whether an approximation rather than equality is intended. Substitution can be algebraically correct yet technically wrong when assumptions fail or the population or system boundary changes. Validity limit: The sampling theorem assumes a strictly band-limited signal and ideal uniform sampling. Practical systems need anti-aliasing filters and margin because real filters do not have a perfect cutoff. Below the Source: MIT OpenCourseWare 6.003, Signals and Systems, sampling and reconstruction lecture materials.
The stated units are: fs and fmax in Hz. Convert values to a consistent unit system before substitution; counts, percentages and dimensionless ratios are not interchangeable. The variable list states the role of each symbol. Dimensional analysis catches many errors but does not replace checking the formula's assumptions. Validity limit: The sampling theorem assumes a strictly band-limited signal and ideal uniform sampling. Practical systems need anti-aliasing filters and margin because real filters do not have a perfect cutoff. Below the Source: MIT OpenCourseWare 6.003, Signals and Systems, sampling and reconstruction lecture materials.
Comparison helps when both quantities address the same question but emphasize different properties. Report the definition, input data, threshold or averaging with the value. The source MIT OpenCourseWare 6.003, Signals and Systems, sampling and reconstruction lecture materials. supports the definition used here; other conventions can differ. Choose the measure to match the learning or analysis goal. Validity limit: The sampling theorem assumes a strictly band-limited signal and ideal uniform sampling. Practical systems need anti-aliasing filters and margin because real filters do not have a perfect cutoff. Below the Source: MIT OpenCourseWare 6.003, Signals and Systems, sampling and reconstruction lecture materials.
Quanta exam set
Curated exam set for "Nyquist–Shannon sampling limit":
Question (front)
Which formula describes Nyquist–Shannon sampling limit?
Answer in your set
Question (front)
How do you rearrange Nyquist–Shannon sampling limit for Defining relation?
Answer in your set
Question (front)
Which common mistake happens with Nyquist–Shannon sampling limit?
Answer in your set
+ 7 more cards: units, variables, derivation, example, exam task
The formula set contains 10 cards. After importing, review them and start practicing; your ratings determine later review intervals.
This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.
Create a curated FSRS exam set for Abtastfrequenz fs > 2 · maximale Signalfrequenz fmax: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
Curated formula set · LaTeX · FSRS spaced repetition · import from Essential