The　rotational　frequency　(RF)　is　an　important　information　for　multi-fault　features　detection　of　rolling　bearing　under　varying　speed　conditions.　In　the　traditional　methods,　such　as　the　computed　order　analysis　(COA)　and　the　time-frequency　analysis　(TFA),　the　RF　should　be　measured　using　an　encoder　or　extracted　by　a　complex　algorithm,　which　bring　challenge　to　bearing　fault　diagnosis.　In　order　to　address　this　issue,　a　novel　iterative　generalized　demodulation　(IGD)　based　method　guided　by　the　instantaneous　fault　characteristic　frequency　(IFCF)　extraction　and　enhanced　instantaneous　rotational　frequency　(IRF)　matching　is　proposed　in　this　paper.　Specifically,　the　resonance　frequency　band　excited　by　bearing　fault　is　first　obtained　by　the　band-pass　filter,　and　its　envelope　time-frequency　representation　(TFR)　is　calculated　using　the　Hilbert　transform　and　the　short-time　Fourier　transform　(STFT).　Second,　the　IFCF　is　extracted　using　the　harmonic　summation-based　peak　search　algorithm　from　the　envelope　TFR.　Third,　the　time-varying　RF　ridge　is　transformed　into　a　line　paralleling　to　the　time　axis　using　the　IGD　with　the　phase　function　(PF).　The　PF　is　calculated　by　the　IFCF　function　and　fault　characteristic　coefficient　(FCC).　Lastly,　the　iterative　generalized　demodulation　spectrum　(IGDS)　is　obtained　using　the　fast　Fourier　transform　(FFT)　for　identifying　fault　type　corresponding　to　the　extracted　IFCF.　Based　on　obtained　fault　type　and　FCC　ratios,　new　PFs　and　frequency　points　(FPs)　are　calculated　for　detecting　other　faults.　Both　simulated　and　experimental　results　validate　that　multi-fault　features　of　rolling　bearing　under　time-varying　rotational　speeds　can　be　effectively　identified　without　RF　measurement　and　extraction.(c)　2022　ISA.　Published　by　Elsevier　Ltd.　All　rights　reserved.