The modeling of neural systems often involves representing the temporal structure of a dynamic stimulus. We extend the methods of the Neural Engineering Framework (NEF) to generate recurrently connected populations of spiking neurons that compute functions across the history of a time-varying signal, in a biologically plausible neural network. To demonstrate the method, we propose a novel construction to approximate a pure delay, and use that approximation to build a network that represents a finite history (sliding window) of its input. Specifically, we solve for the state-space representation of a pure time-delay filter using Pade-approximants, and then map this system onto the dynamics of a recurrently connected population. The construction is robust to noisy inputs over a range of frequencies, and can be used with a variety of neuron models including: leaky integrate-and-fire, rectified linear, and Izhikevich neurons. Furthermore, we extend the approach to handle various models of the post-synaptic current (PSC), and characterize the effects of the PSC model on overall dynamics. Finally, we show that each delay may be modulated by an external input to scale the spacing of the sliding window on-the-fly. We demonstrate this by transforming the sliding window to compute filters that are linear (e.g., discrete Fourier transform) and nonlinear (e.g., mean squared power), with controllable frequency.