Resampling

Resampling encompasses techniques for generating new samples or estimates from existing data or signals by changing the sampling rate or by repeatedly drawing from the observed data. In statistics, resampling uses the observed data as a stand-in for the population to assess uncertainty or to validate models. In digital signal processing, resampling changes the sampling rate of a discrete-time signal, typically by interpolation to raise the rate or by decimation to lower it.

Statistical resampling methods include bootstrapping, which forms many samples with replacement to approximate sampling distributions; permutation tests, which shuffle data to test null hypotheses; and cross-validation, which partitions data into training and validation sets repeatedly to estimate predictive performance.

Signal resampling involves upsampling, where the sampling rate is increased by inserting new samples and often filtering to suppress imaging artifacts; and downsampling, where the rate is reduced with a low-pass anti-alias filter. Interpolation methods range from nearest neighbor and linear to high-order schemes, including spline and sinc-based approaches.

Resampling also appears in time series and image processing, where resolution or frequency is changed by aggregation (for example, averaging blocks) or interpolation-based resizing. The method choice affects accuracy, smoothness, and computational cost.

Practical considerations include accounting for data dependence (block resampling for time series), avoiding aliasing, and ensuring reproducibility via random seeds. Resampling is a versatile tool for estimating uncertainty, assessing models, and adapting data to different analysis or processing requirements.