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Recently, neural fields, also known as coordinate-based MLPs, have achieved impressive results in representing low-dimensional data. Unlike CNN, 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 conversely a recovering operator that provides better controllability for local adjustments. We have found that using either operator alone can 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 regions overly smoothed. In this way, our filter helps neural fields remove much noise while enhancing details. We demonstrate the benefits of our filter on various tasks and show significant improvements over state-of-the-art methods. Moreover, our filter also provides better performance in terms of convergence speed and network stability.