Leakage-free identification of FRF's with the discrete time Fourier transform

The discrete time Fourier transform (DTFT) has for long been used for non-parametric measurement of frequency response functions (FRF). However, beyond the appreciable simplicity and computational efficiency of the method, its use has been severely criticised when applied to stationary random signals because of the inherent spectral leakage it induces—e.g. in the so-called H1H1, H2H2, H3H3, HvHv, etc. estimators. This problem is one major reason which has motivated recent research on alternative identification methods, always at the price of increased complexity. This paper aims at demonstrating that, contrary to the common belief, solutions do exist for designing low-bias, or even unbiased, i.e. leakage free, FRF estimators based on the DTFT of stationary random signals. One such solution was proposed 25 years ago by Rabiner and has surprisingly remained unknown by mechanical engineers concerned with system identification. We first give a brief review of the principles which underlie Rabiner's method. We next present original analytical results, which exactly specify under which conditions Rabiner's estimator is unbiased, and we also provide the expression of its variance. These results then lead to a number of practical guidelines. The actual validity of the method is finally illustrated on some examples, and compared with other more classical estimators.