Non-linear analysis of a linear-non-linear-linear system

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Abstract
There are many non-linear systems in the field of biological systems, control systems and communication systems. The identification of non-linear system is a fundamental problem in these fields. Many investigations of non-linear systems have been carried out from the viewpoint of parameter identification. The so-called general model has been well studied in non-linear identification problems. The general model is a memoryless non-linearity sandwiched between two linear time-invariant subsystems. In biological systems, this model is applicable to retinal neurons in visual information processing. In physically realizable systems, we need to consider a causal system. Based on input-output causality, we develop a new complete identification method for the general model in the discrete time domain. Further, we derive a new formula for the estimation of non-linear parameters in the general model. The method developed here is simpler than conventional identification procedures. Finally, the results are simulated to verify our identification method.

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