Optimal sampling interval for system identification based on decimation and interpolation

To improve the mean square error (MSE) of the least squares (LS) estimate of an impulse response, a new approach to signal sampling and measurement is proposed, based on decimation and interpolation. It is analytically shown that there exists an optimal sampling interval which can minimise the MSE, and this optimal sampling interval depends on the impulse response, the input power spectrum or the eigenvalues´ distribution of the correlation matrix of the input signal, the noise variance and the total number of data. Furthermore, an effective data-based scheme to determine the optimal sampling interval is given by using the only accessible input-output data. The effectiveness of the presented algorithm is demonstrated through numerical examples