User:Eub~enwiki/scratch

Stages of resampling

signal	in the time domain	in the frequency domain
(1) $x[n]$ The original discrete-time signal, sampled at $f_s$.
(2) $x_{\delta }(t)=\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}x[n]\delta (t-n/f_s)$ Construct a continuous-time signal by placing a unit impulse for each sample.
(3) $x^{\prime }(t)=\text{lowpass}(x_{\delta },f{\text{'}}_s/2)$
(4) $x^{\prime }[n]=x^{\prime }(n/f{\text{'}}_s)$ Create the desired discrete-time signal (4) by sampling the signal (3) at appropriate times. This $x^{\prime }[n]$ is $x[n]$ resampled to the new sampling rate$f{\text{'}}_s$.

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Resampling is a term used in statistics to describe a variety of methods for computing summary statistics using subsets of available data (jackknife), drawing randomly with replacement from a set of data points (bootstrapping), or switching labels on data points when performing significance tests (permutation test).

Resampling in digital signal processing refers to converting a sampled signal from one sampling frequency to another. For instance, the output waveform of a DAW that processes at 96 kHz would have to be resampled to 44.1 kHz to be placed on a CD.

These two concepts are related.