Noise limitations of system identification techniques

Three practical identification techniques are analyzed, and the time required by each of these techniques to estimate, in the presence of noise, the impulse response of an unknown system, within a specified accuracy, is determined. The identification time can be expressed in each case as the product of twice the gain-bandwidth product of the system being identified, divided by the variance of the estimate times the output SNR. The equivalence of the three methods is discussed and it is shown that the identification time of these methods represents the minimum identification time when a priori knowledge about the unknown system is not available.