Analyzing Measurements of Nonlinear Transfer Functions with Tschebyshev Polynomials

Recently, due to advances in computers and data aquisition systems, the following type of measurement has become more common: (1) Impress a given modulation on a device to be tested. (2) Acquire a data stream, usually at equally spaced sample intervals, of the response of the system to the modulation. (3) Fit the data thereby acquired to some nonlinear function set that might (or might not!) describe the response of the device. In this paper it is pointed out that by choosing to modulate the test parameter sinusoidally, and by fast-Fourier transforming the acquired data stream, one unambiguously determines the Tschebyshev expansion of the response function around the working point, potentially yielding quantitative information about high nonlinear orders in the system response. The need for data fitting is thereby eliminated. A detailed example, the analysis of the nonlinear phase-phase transfer function in the Jefferson Lab injector, is presented.