| Abstrakt: |
Random phase multisines tend asymptotically, with an increasing number of harmonics and irrespective of their spectral coloring, to the Gaussian amplitude distribution and can be used as an alternative to Gaussian signals to measure the best linear approximation (BLA) of nonlinear systems. The asymptotic error on the measured frequency characteristics, compared to that measured with Gaussian noise, is of order $O(M^{-1})$ , where $M$ is the number of harmonics. Flat (white) multisines are still a better approximant to Gaussian noise, because even in a nonasymptotic setting ($M$ is low), the measured BLA of a static nonlinearity remains static. This is due to the fact that both Gaussian noise and flat random phase multisines are separable signals. Random phase multisines with a nonflat spectral coloring, however, are nonseparable signals and introduce dynamics to the BLA of a static nonlinearity, which was observed for a low harmonic number. Due to this reason, usually, only flat random phase multisines are used in the applications. In this paper, we investigate more deeply this phenomenon, performing an order $O(M^{-2})$ analysis of the approximation error. We show that the dynamics of the error depend, in a simple way, on the spectral coloring and this effect is decaying quickly with increasing $M$. We conclude, in consequence, that colored random phase multisines are asymptotically a good working alternative to Gaussian noise and even a better choice for an excitation than flat random phase multisines due to more freedom in a signal design. [ABSTRACT FROM AUTHOR] |
