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The authors introduce a new identification method for general causal convolution models of the form u → h * u = H(∂t)u, where h is the impulse response of the system, to be identified from measurement data. This method is based on a suitable parameterisation of operator H(∂t) deduced from the so-called diffusive representation, devoted to state representations of such integral operators. Following this approach, the complex dynamic features of H(∂t) can be summarised by a few numerical parameters on which the identification method will focus. The class of concerned convolution operators includes rational as well as non-rational ones, even of complex nature. For illustration, we implement this method on a numerical example.