Optimal sampling rate for impulse response identification based on decimation and interpolation

High-rate sampled input-output data does not necessarily provide better mean squares error (MSE) for a least squares (LS) estimate of impulse response. The authors propose a scheme to improve the MSE by decimating the high-rate sampled input-output data, calculating the LS estimate of the decimated impulse response, and interpolating the estimate to recover the LS estimate with the original high sampling rate. They clarify the existence of the optimal sampling rate that minimizes the MSE of the interpolated estimate, and propose an efficient scheme for determining the optimal sampling rate without using the unknown true values of the frequency response to be identified and the noise variance but using only accessible input-output data.<>