Neural　fields,　also　known　as　coordinate-based　multi-layer　perceptrons　(MLPs),　have　recently　achieved　impressive　results　in　representing　low-dimensional　data.　Unlike　convolutional　neural　networks　(CNNs),　MLPs　are　globally　connected　and　lack　local　control;　adjusting　a　local　region　leads　to　global　changes.　Therefore,　improving　local　neural　fields　usually　leads　to　a　dilemma:　filtering　out　local　artifacts　can　simultaneously　smooth　away　desired　details.　Our　solution　is　a　new　filtering　technique　that　consists　of　two　counteractive　operators:　a　smoothing　operator　that　provides　global　smoothing　for　better　generalization　and　a　recovery　operator　that　provides　better　controllability　for　local　adjustments.　We　found　that　using　either　operator　alone　could　lead　to　an　increase　in　noisy　artifacts　or　oversmoothed　regions.　By　combining　the　two　operators,　smoothing　and　sharpening　can　be　adjusted　to　first　smooth　the　entire　region　and　then　recover　fine-grained　details　in　the　overly　smoothed　regions.　Thus,　our　filter　helps　neural　fields　remove　significant　noise　while　enhancing　the　details.　We　demonstrate　the　benefits　of　our　filter　on　various　tasks,　where　it　shows　significant　improvements　over　state-of-the-art　methods.　Moreover,　our　filter　provides　a　better　performance　in　terms　of　convergence　speed　and　network　stability.