# Bias Removal in Higher Order Sinusoidal Input Describing Functions

TL;DR: A novel method is presented for the reduction of bias caused by harmonic excitation in the identification of higher order sinusoidal input describing functions (HOSIDF) and is demonstrated with real measurements on a mechanical system with friction.

Abstract: In this paper a novel method is presented for the reduction of bias caused by harmonic excitation in the identification of higher order sinusoidal input describing functions (HOSIDF). HOSIDF are a recently introduced generalization of the theory of the describing function. HOSIDF describe the magnitude and phase relations between the individual harmonic components in the output signal of a non-linear system and the sinusoidal excitation signal. In the presented method, the output signal of a non-linear system subjected to harmonic excitation is numerically split up into a fraction caused by the non-linear response due to the fundamental input signal component and the fraction caused by the quasi-linear response due to the harmonic input signal components. This separation is based on the assumption that the non-linear effects of intermodulation can be neglected, compared to the the effects caused by the generation of harmonics and gain compression/expansion. The method is demonstrated with real measurements on a mechanical system with friction.

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### "Bias Removal in Higher Order Sinuso..." refers background in this paper

...the convolution integral description of the linear system can be generalized to an infinite series called the Volterra series [9], [10], [11]....

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### "Bias Removal in Higher Order Sinuso..." refers methods in this paper

...The n-dimensional Fourier transform of the n-th order Volterra kernel yields the n-th-order FRF, the Generalized Frequency Response Function (GFRF) [12], [13]....

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