A computer implemented method for implementing an artificial neural network for dynamic computing applications on a given computing system having an arbitrary synaptic filter H, the artificial neural network comprising a plurality of nodes, each node having a node input and a node output, and the plurality of nodes being arranged into at least one layer of nodes, the method comprising: (a) determining a dynamic function f to be computed using the artificial neural network; (b) defining at least one node response function for the plurality of nodes of the artificial neural network, wherein the at least one node response function is defined to receive varying inputs over time at each node input and produce varying outputs over time at each node output; (c) associating at least one linear synaptic filter with the plurality of nodes, wherein at least one particular linear synaptic filter in the at least one linear synaptic filter is associated with each node in the plurality of nodes to implement the system dynamics of the artificial neural network; (d) accounting for the arbitrary synaptic filter H of the given computing system by: (i) determining a modified dynamic function f ' based on the dynamic function f and the arbitrary synaptic filter H according to: f ′ x u = ∑ i = 0 k c i x i where the arbitrary synaptic filter H of the given computing system is a continuous-time linear synaptic filter, or f ′ x u = ∑ i = 0 k c ̄ i x t + i where the arbitrary synaptic filter H of the given computing system is a discrete-time linear synaptic filter where c i are coefficients of the filter, x represents a system state, u represents a system input, and x ( i) denotes the i th derivative of x (t); (e) determining connection weights between the layers of nodes in the artificial neural network to match the modified dynamic function f ' using the at least one node response function and the at least one linear synaptic filter; and (f) operating the artificial neural network on the given computing system using the determined connected weights to compute the dynamic function f on an auditory or a video or a sensory feedback input for providing a delay, a distortion reversal, high-pass filtering, differentiation or prediction of a future state. (a) determining a dynamic function f to be computed using the artificial neural network; (b) defining at least one node response function for the plurality of nodes of the artificial neural network, wherein the at least one node response function is defined to receive varying inputs over time at each node input and produce varying outputs over time at each node output; (c) associating at least one linear synaptic filter with the plurality of nodes, wherein at least one particular linear synaptic filter in the at least one linear synaptic filter is associated with each node in the plurality of nodes to implement the system dynamics of the artificial neural network; (d) accounting for the arbitrary synaptic filter H of the given computing system by: (i) determining a modified dynamic function f ' based on the dynamic function f and the arbitrary synaptic filter H according to: f ′ x u = ∑ i = 0 k c i x i where the arbitrary synaptic filter H of the given computing system is a continuous-time linear synaptic filter, or f ′ x u = ∑ i = 0 k c ̄ i x t + i where the arbitrary synaptic filter H of the given computing system is a discrete-time linear synaptic filter where c i are coefficients of the filter, x represents a system state, u represents a system input, and x ( i) denotes the i th derivative of x (t); (i) determining a modified dynamic function f ' based on the dynamic function f and the arbitrary synaptic filter H according to: f ′ x u = ∑ i = 0 k c i x i where the arbitrary synaptic filter H of the given computing system is a continuous-time linear synaptic filter, or f ′ x u = ∑ i = 0 k c ̄ i x t + i where the arbitrary synaptic filter H of the given computing system is a discrete-time linear synaptic filter where c i are coefficients of the filter, x represents a system state, u represents a system input, and x ( i) denotes the i th derivative of x (t); f ′ x u = ∑ i = 0 k c i x i where the arbitrary synaptic filter H of the given computing system is a continuous-time linear synaptic filter, or f ′ x u = ∑ i = 0 k c ̄ i x t + i where the arbitrary synaptic filter H of the given computing system is a discrete-time linear synaptic filter where c i are coefficients of the filter, x represents a system state, u represents a system input, and x ( i) denotes the i th derivative of x (t); (e) determining connection weights between the layers of nodes in the artificial neural network to match the modified dynamic function f ' using the at least one node response function and the at least one linear synaptic filter; and (f) operating the artificial neural network on the given computing system using the determined connected weights to compute the dynamic function f on an auditory or a video or a sensory feedback input for providing a delay, a distortion reversal, high-pass filtering, differentiation or prediction of a future state.