为了更好地恢复亚奈奎斯特图像以减少失真，选择好的内插模板是关键。通过对一种新的一维频率域重叠数字滤波器的理论分析，找到了对应的 FIR滤波器模型和线性相位的满足条件。据此给出二维 Fourier加窗内插模板的设计方案。对 7× 7无窗、单窗和双窗 3种模板的传输特性进行了比较，指出带窗模板在通带区域内波纹起伏明显少于无窗模板。 3种带窗模板中，双窗的平滑性优于单窗和无窗，但具有较大的过渡沿。分别用 7× 7、11× 11和 17× 17阶模板对具有不同频率分布的亚采样灰度图像进行了内插处理模拟实验，并对结果进行了分析和比较，验证了用带窗模板恢复亚奈图像可以获得较高的信噪比，提高了恢复图像的主客观质量

Choosing a good interpolating template is the key to better recover the subsampled image with low distortion. In this paper, by analysis of a novel 1-dimension overlapping digital filter in frequency domain, the corresponding model of FIR filter and the condition for linear phrase are presented. According to the above result, the ways to design 2-dimension interpolating template without window、with single and double windows are respectively introduced. Transmission properties of 7×7 templates of three systems are compared in detail, which indicates that the ripples in the pass period of windowed template are obviously much fewer than that of template without window. Among the three types of systems, template with double windows is better than that of single window and none window in smoothness but has the widest transition period. Finally, the simulations to recover the subsampled images with different frequency components by applying 7×7、11×11 and 17×17 templates are made, as well as analyzing and comparing the results. It proves that the images recovered by three types of windowed templates from subsampled image have higher SNR and better subjective and objective quality than that recovered in no overlapping way.