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.
Understanding this principle is crucial for designing systems that accurately digitize continuous-time signals without losing information.
Related concepts
aliasing is: high frequencies masquerading as low frequencies due to undersampling
Aliasing occurs when high frequencies masquerade as low frequencies due to undersampling
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
Rate-distortion theory: minimum bits to represent data within distortion D
Rate-distortion theory: minimum bits to represent data within distortion D = R(D)
Shannon's source coding theorem: you can't compress below entropy
Shannon's theorem: Data compression can't exceed entropy limit
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