# 描述函数

## 原理

${\displaystyle g(A,\,j\omega )={\frac {1}{\pi A}}\int _{0}^{2\pi }f(A\sin \omega t)\sin \omega td\omega t}$
${\displaystyle b(A,\,j\omega )={\frac {1}{\pi A}}\int _{0}^{2\pi }f(A\sin \omega t)\cos \omega td\omega t}$

## 延伸阅读

• N. Krylov and N. Bogolyubov: Introduction to Nonlinear Mechanics, Princeton University Press, 1947
• A. Gelb and W. E. Vander Velde: Multiple-Input Describing Functions and Nonlinear System Design, McGraw Hill, 1968.
• James K. Roberge, Operational Amplifiers: Theory and Practice, chapter 6: Non-Linear Systems, 1975; free copy courtesy of MIT OpenCourseWare 6.010 (2013); see also (1985) video recording of Roberge's lecture on describing functions
• P.W.J.M. Nuij, O.H. Bosgra, M. Steinbuch, Higher Order Sinusoidal Input Describing Functions for the Analysis of Nonlinear Systems with Harmonic Responses, Mechanical Systems and Signal Processing, 20(8), 1883–1904, (2006)