In　fault　detection,　feedback　control,　and　other　fields,　real-time　differential　estimation　of　a　given　signal　in　a　complex　noise　environment　is　an　important　but　challenging　task.　In　this　paper,　a　discrete-time　fast　nonlinear　tracking　differentiator　(FNTD)　based　on　hyperbolic　tangent　functions　was　proposed.　To　start,　the　differential　signal　acquisition　problem　was　equated　to　the　time-optimal　control　(TOC)　law　for　constructing　a　double-integral　system　using　a　state　feedback　approach.　Next,　the　FNTD　algorithm　based　on　the　hyperbolic　tangent　function　was　presented　by　utilizing　the　isochronic　region　(IR)　method　in　the　discrete　time　domain.　Then,　the　frequency-domain　characteristics　of　the　FNTD　were　analyzed　and　the　rule　for　tuning　the　parameters　was　provided　by　the　frequency　scan　test　method.　Finally,　the　simulation　results　demonstrated　that　the　proposed　FNTD　had　fast　and　accurate　tracking　performance,　as　well　as　excellent　filtering　and　differential　extraction　capability　compared　with　other　differentiators.