Spectral distortion in sampling rate conversion by zero-order polynomial interpolation

For such applications as digital beamforming in sonar and sampling rate conversion in digital audio systems, there is interest in fast, approximate interpolation techniques. Computationally, the simplest of these is to approximate the desired time series sample by the available sample which is nearest in time. This procedure is variously known as sample-and-hold interpolation, zero-order polynomial interpolation, or selective subsampling. The effect of this approximation on signal-to-noise ratio has already been addressed in the literature. This correspondence extends those previous analyses by deriving the spectral characteristics of the noise generated. It is shown that, because the timing errors involved in zero-order polynomial interpolation are not random, the effect on the input spectrum is not simply to broaden it by the transfer of power from narrowband signal components to broadband noise, from narrowband signals to narrowband noise or distortion components