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We present a two-dimensional higher order FDTD algorithm to minimize the numerical dispersion error at arbitrary, preassigned angles. Filtering schemes are further employed to optimize the FDTD frequency response at a given frequency range. A stability analysis of the resulting FDTD algorithms is included. Numerical dispersion properties are compared against Yee's scheme and a higher order (2,4) FDTD scheme. Numerical results demonstrate that the dispersion error around a preassigned angle (and, with filtering, around a frequency band of choice) can be significantly reduced.