Suki B, Lutchen K R
Department of Biomedical Engineering, Boston University, MA 02215.
IEEE Trans Biomed Eng. 1992 Nov;39(11):1142-51. doi: 10.1109/10.168693.
There is an increasing need in physiology to estimate nonparametric linear transfer functions from data originating from biological systems which are invariably nonlinear. For pseudorandom (PRN) input stimuli, we derive general expressions for the apparent transfer (Z) and coherence (gamma 2) functions of nonlinear systems that can be represented by a Volterra series. It is shown that in the case of PRN signals in which the frequency components are integer multiples of other components the estimates of Z are seriously biased due to harmonic distortion and crosstalk among frequency components of the input. When the PRN signal includes components that are not integer multiples of other components harmonic distortion is avoided, but not necessarily cross talk. Here the estimates of Z remain poor without a noticeable influence on gamma 2. To avoid the problems associated with harmonic distortions and minimize the influence of crosstalk, a family of pseudorandom signals is proposed which are especially suited for the estimation of Z and gamma 2 in mechanical measurements of physiological systems at low frequencies. The components in the signals cannot be reproduced as linear combinations of two or more frequency components of the input. In a second-order system, this completely eliminates the bias, while in higher-order, but not strongly nonlinear systems, the interactions among the components are reduced to a level that the response can be considered as if it was measured with independent sine waves of an equivalent amplitude. It is also shown that the values of gamma 2 are not appropriate to assess linearity of the system. The theory is supported by simulation results and experimental examples brought from the field of respiratory mechanics by comparing the input impedance of the respiratory system of a dog measured with various PRN signals.
在生理学中，越来越需要从本质上是非线性的生物系统产生的数据中估计非参数线性传递函数。对于伪随机（PRN）输入刺激，我们推导了可以用沃尔泰拉级数表示的非线性系统的表观传递（Z）函数和相干（γ2）函数的一般表达式。结果表明，在频率分量是其他分量整数倍的PRN信号情况下，由于输入频率分量之间的谐波失真和串扰，Z的估计存在严重偏差。当PRN信号包含不是其他分量整数倍的分量时，可避免谐波失真，但不一定能避免串扰。此时，Z的估计仍然很差，而对γ2没有明显影响。为了避免与谐波失真相关的问题并最小化串扰的影响，提出了一类伪随机信号，它们特别适合于在低频下对生理系统进行机械测量时估计Z和γ2。信号中的分量不能作为输入的两个或多个频率分量的线性组合再现。在二阶系统中，这完全消除了偏差，而在高阶但不是强非线性系统中，分量之间的相互作用降低到可以将响应视为用等效幅度的独立正弦波测量的水平。还表明，γ2的值不适用于评估系统的线性度。通过比较用各种PRN信号测量的狗的呼吸系统的输入阻抗，仿真结果和呼吸力学领域的实验示例支持了该理论。
