Network filtering is a technique to isolate core subnetworks of large and complex interconnected systems, which has recently found many applications in financial, biological, physical and technological networks among others. We introduce a new technique to filter large dimensional networks arising out of dynamical behavior of the constituent nodes, exploiting their spectral properties. As opposed to the well known network filters that rely on preserving key topological properties of the realized network, our method treats the spectrum as the fundamental object and preserves spectral properties. Applying asymptotic theory of high-dimensional covariance matrix estimation, we show that the proposed filter can be tuned to interpolate between zero filtering to maximal filtering that induces sparsity via thresholding, while having the least spectral distance from a consistent (non-)linear shrinkage estimator. We demonstrate the application of our proposed filter by applying it to covariance networks constructed from financial data, to extract core subnetworks embedded in full networks.