Pertaining to dynamic systems in general,a review is given of relations between mathematical descriptions in the frequency domain or time domain and state-space descriptions.For the analysis of hydrodynamic problems in ocean engineering wave forces may be represented by convolution integrals.The paper presents a method to construct a finite-order state-space model which represents a good approximation to such a convolution integral.The method utilizes a particular algorithm to compute the partial derivative of the exponential function of a(state-space)matrix with respect to the matrix elements.The method is applied to an example of fitting a state space model of order five to the free oscillations corresponding to wave radiation in a transient experiment with an oscillating water column. Pertaining to dynamic systems in general, a review is given of relations between mathematical descriptions in the frequency domain or time domain and state-space descriptions.For the analysis of hydrodynamic problems in ocean engineering wave forces may be represented by convolution integrals.The paper presents a method to construct a finite-order state-space model which represents a good approximation to such a convolution integral. The method utilizes a particular algorithm to compute the partial derivative of the exponential function of a (state-space) matrix with respect to the matrix elements. The method is applied to an example of fitting a state space model of order five to the free oscillations corresponding to wave radiation in a transient experiment with an oscillating water column.