In　response　to　a　series　of　problems　such　as　high　computational　complexity,　slow　processing　speed,　poor　denoising　effect,　signal　loss,　energy　attenuation,　and　decreased　transmission　performance　that　traditional　filtering　methods　face　when　filtering　digital　signals　from　electronic　measuring　instruments　in　the　laboratory,　a　fast　filtering　method　for　digital　signals　of　electronic　measuring　instruments　in　the　laboratory　on　the　basis　of　the　Fourier　transform　is　studied.　Based　on　the　Fourier　transform,　an　adaptive　time–frequency　filtering　method　based　on　the　fractional　Fourier　transform　is　proposed.　By　utilizing　the　important　characteristic　that　this　transform　is　equivalent　to　rotating　the　signal　in　the　time–frequency　plane,　mixed　noisy　signals　are　subjected　to　a　fractional　Fourier　transform　at　a　specific　rotation　angle　to　minimize　the　overlap　between　the　signal　and　noise　in　the　transform　domain.　The　linear　frequency　modulation　(LFM)　signal　is　filtered　and　extracted　through　fractional　Fourier　transform　method.　Most　of　the　noise　energy　is　removed,　and　the　original　LFM　signal　is　recovered　by　fractional　Fourier　inverse　transform　to　realize　the　rapid　filtering　of　high-quality　digital　signals　of　electronic　measuring　instruments　in　the　laboratory.　Experiments　have　shown　that　using　this　filtering　method　to　denoise　digital　signals　from　laboratory　electronic　measuring　instruments　can　not　only　reduce　computational　complexity,　improve　filtering　speed,　but　also　enhance　filtering　effectiveness.　The　filtered　signal　has　low　noise　content,　high　restoration,　good　transmission　performance,　reduced　attenuation,　and　strong　anti-interference　ability.　At　the　same　time,　it　can　effectively　remove　various　types　of　noise,　with　an　average　improvement　percentage　of　15.68%　in　signal-to-noise　ratio.　It　also　maintains　the　integrity　of　data　sampling　and　the　accuracy　of　statistical　results,　which　is　conducive　to　further　analysis　and　research.　©　The　Author(s),　under　exclusive　licence　to　Springer　Nature　Switzerland　AG　2023.