2nd-order Volterra kernel measurement using pseudorandom ternary signals and discrete Fourier transforms

A method is developed for the measurement of the values of a 2nd-order kernel in a Volterra-series representation of a nonlinear system, using the discrete Fourier transform of the system output sequence when the system input is an antisymmetric pseudorandom ternary signal. It is shown that the inverse transform of a product of the output transform and the transform of the square of the input sequence yields a crosscorrelation function from which estimates of the 2nd-order kernel values may be obtained by an established procedure. Properties of the discrete Fourier transform of the square of an antisymmetric pseudorandom ternary sequence are developed and used in a comprehensive procedure for estimating the linear frequency response, 1st-order kernel and 2nd-order kernel of a system with minimal computation.