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　f　sa)　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　f　s　a　based　TD　outperforms　the　fhan　based　TD　in　both　filtering　and　differentiation　©　2024　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.