Measurement of frequency responses of nonlinearly distorted SISO systems in noisy environments with generalized parameter frequency response estimators

Topic of this paper is the measurement of frequency responses of SISO systems in the presence of nonlinear system distortions and measurement noise. The measurement uses periodic test signals and digital signal processing. Nonlinear distortion contributions and noise will be modelled by two noise sources which are located at system input and at system output. The justification of modelling the deterministic distortion contributions as (random) noise is given in the appendix. The criteria of test signal design will be discussed and appropriate test signals will be proposed. The known frequency response estimators H1H1, H2H2, HrHr(H3)(H3) and HvHv are motivated, compared and the systematic estimation errors are computed. In addition, generalized parameter frequency response estimators are proposed. A way of deriving generalized parameter frequency response estimators will be introduced in this paper. This way offers particular transparency. The generalized estimators include the known estimators are special cases and they can be adapted to the distortion characteristics which makes these estimators to candidates for the desired universal estimators.