In this paper, a general feedback structure is proposed to improve the performance of existing digital notch filters. With the feedback structure, the notch filter can have a narrower stopband. This structure can be applied to any type of existing notch filter. We first derive the improved design of existing one-dimensional (1-D) filters. Then, by suitably extending the 1-D concept, the design of two-dimensional (2-D) notch filters is also derived. To demonstrate the effectiveness of the proposed design, an experiment on the interference removal of an image is presented. Moreover, a new forward and reverse algorithm for 2-D image filtering is proposed to reduce the transient error and enhance the signal-to-noise ratio drastically.