Sample at ≥ 2× the highest frequency to avoid aliasing
Nyquist–Shannon sampling theorem
Sample at ≥ 2× the highest frequency to avoid aliasing
The Nyquist-Shannon sampling theorem provides a sufficient condition for perfect fidelity in signal reconstruction. It states that a sample rate must be at least twice the highest frequency present in the signal to capture all the information without loss.
Example
If a signal contains frequencies up to 1 kHz, sampling at 2 kHz or higher is necessary to avoid aliasing and ensure accurate reconstruction of the original signal.
Remember this
Understanding this principle is crucial for designing systems that accurately digitize continuous-time signals without losing information.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
Related concepts
aliasing is: high frequencies masquerading as low frequencies due to undersampling
Aliasing occurs when sampling frequency is less than twice the highest frequency component (f_s < 2f_max)
Minimum-variance unbiased estimator
MVUE achieves lower variance than any other unbiased estimator
Central limit theorem
Central limit theorem states that sample means converge to normal distribution as sample size increases
Principal component analysis
Eigenvectors point along maximum variance
Norm (mathematics)
L∞ norm equals max absolute value
Manifold hypothesis
High-dimensional data lies on lower-dimensional manifolds
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