A sparse third-order orthogonal frequency-domain Volterra-like model

The purpose of this paper is twofold. The first objective is to develop a discrete frequency-domain orthogonal third-order Volterra model valid for both nonGaussian and Gaussian stationary random inputs in order to eliminate the presence of ‘interference’ terms. The second objective is to develop a sparse third-order frequency-domain Volterra model by identifying the most significant frequency-domain Volterra kernel coefficients using a given amount of raw experimental times series data. The concept of coherence function is extended to the orthogonal higher-order model in order to quantify the goodness of both the model and its constituent linear, quadratic, and cubic components and, then, is utilized as a criterion to select the most significant frequency-domain Volterra kernel coefficients to be included in the sparse Volterra model. Identification of the most significant frequency-domain Volterra coefficients is based upon a frequency-domain extension of the well-known orthogonal-search method. Finally, the practicality and feasibility of these approaches are demonstrated by utilizing them to model actual physical nonlinear systems given experimental input-output data from such systems.