Minimum gain identifiable when pseudo-random binary sequences are used for system identification in noisy conditions

A method to determine the minimum gain of the system is presented which can be identified by pseudorandom binary sequence (PRBS)- based approaches when noise is present in the output signal. A formula for the minimum gain is derived in terms of required noise resilience from the discrete Fourier transforms of the PRBS signals and white noise. The formula allows an engineer to discount noiseaffected low-gain portions of the transfer function. The calculated minimum gain is compared graphically with noisy Bode plots and good agreement is shown with the actual noise level, demonstrating the usefulness of the result.