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Vandermonde Method for Separation of Nonlinear Orders and Measurement of Linear Response

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The Vandermonde matrix method for separation of nonlinear components and full-power linear response measurement is analyzed in this paper. This technique involves making several measurements of a nonlinear system (a woofer or horn system for example) at different gains and applying the inverse Vandermonde gain matrix to the vector of outputs. The Vandermonde matrix method does more than just return the linear response, as it more generally separates all of the nonlinear orders breaking difficult nonlinear system estimation tasks into more tractable problems, one for each Volterra kernel. Quantitative measures for the degree of nonlinear order separation are proposed. The Vandermonde matrix order separation method is analyzed for noise robustness and gain spacing sensitivity and found to be a useful and practical tool for audio measurements.

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