Real-time　filtering　and　derivative　signals　with　as　small　phase　lag　as　possible　are　of　great　significance　for　control　performances.　In　this　work,　an　enhanced　time　optimal　control　(referred　as　fsa)　based　tracking　differentiator　(TD)　is　proposed,　which　can　guarantee　a　small　phase　lag　in　both　filtering　and　differential　signals　for　a　class　of　input　signals　with　different　levels　of　noises.　This　characteristic　is　achieved　by　introducing　a　damping　coefficient　to　the　boundary　transformation　function　of　the　time-optimal　control　algorithm.　Simulation　results　show　that　the　proposed　fsa　based　TD　outperforms　the　fhan　based　TD　in　both　filtering　and　differentiation.