By means of the inverse Fourier transform, we introduce an easy way to design convolutional differentiators. Such convolutional spatial differentiators may be used for the pseudo-spectral solution of the scalar wave equation. The tapered differentiators have the same form as a high-order finite difference (FD) operator, and share some of the advantages of both the conventional FD and Fourier methods. The differentiators have been implemented for 2-D zero-offset and common-source seismic modeling. Results using filters with as few as five points are acceptable; longer operators (e.g., 15 points) yield results of comparable quality to seismograms obtained with the Fourier method, but with considerable savings in computer time. Accuracy of the convolutional differentiator approach is appreciably better than that of the fourth-order FD method. The method can readily be extended to elastic wave field modeling.