Aliasing

Aliasing is an error in which undersampling makes distinct signal frequencies appear as lower or different frequencies. It occurs when sampling fails to preserve enough information to distinguish a signal’s oscillations.

Nyquist–Shannon sampling theorem: A theorem specifying conditions under which a continuous band-limited signal can be reconstructed exactly from its samples. Its sampling-rate limit identifies when frequency aliasing can occur.
Anti-aliasing filter: A filter that attenuates frequencies above the range a sampling system can represent. It limits high-frequency input before sampling to prevent false lower frequencies.
Continuous-time signal: A signal defined at every instant of time rather than only at discrete intervals. Aliasing concerns how such signals are represented by discrete samples.
Quantization error: The difference between a signal value and its nearest representable discrete amplitude level. Quantization changes amplitude values; aliasing changes the apparent frequency content.
Compressed sensing: A signal-recovery framework that reconstructs sparse signals from fewer measurements than conventional sampling requires. It challenges simple sampling-rate intuitions but relies on sparsity assumptions, not unrestricted recovery.
Nyquist frequency: Half the sampling rate, marking the highest frequency that can be represented without aliasing under ideal conditions. Frequencies above this boundary fold into lower frequencies.
Oversampling: Sampling a signal at a rate substantially above its minimum required rate. It provides more room for practical filters to suppress frequencies that would alias.
Discrete-time signal: A sequence of values indexed by integer steps, often produced by sampling a continuous signal. Its frequency representation repeats, making distinct continuous frequencies indistinguishable.
Spectral leakage: The spreading of a signal’s spectral energy across frequency bins when analyzing a finite record. It can blur measured frequencies, but it is caused by finite observation windows rather than undersampling.
Nonuniform sampling: Sampling at irregularly spaced times or positions rather than at a fixed interval. Its reconstruction limits differ from uniform sampling, prompting questions about when aliases remain distinguishable.

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