In　engineering　construction　monitoring,　it　is　often　necessary　to　monitor　the　vibration　velocity　signal　or　vibration　acceleration　signal.　The　spectrum　characteristics　of　vibration　velocity　signal　and　vibration　acceleration　signal　are　very　different,　which　will　affect　the　subsequent　analysis.　In　this　paper,　the　time-domain　calculus　of　Fourier　transform　is　adopted　to　analyze　the　sensitivity　of　the　spectrum　of　engineering　vibration　signal.　The　Fourier　spectrum,　self-power　spectrum　and　frequency　response　function　of　structural　vibration　are　obtained　by　Laplace　transform,　and　their　sensitivity　is　analyzed.　The　physical　significance　of　its　differential　sensitivity　is　analyzed　by　frequency　response　function.　The　vibration　signal　of　measured　natural　excitation　in　middle　and　high　buildings　in　the　background　engineering　is　verified,　and　the　influence　of　the　sensitivity　of　spectrum　calculus　on　the　vibration　signal　analysis　is　analyzed.　The　results　show　that:　In　terms　of　mathematics,　the　frequency　distribution　of　the　peak　of　Fourier　spectrum　is　sensitive　to　calculus　due　to　the　time-domain　calculus　nature　of　Fourier　transform.　With　the　increase　of　the　differential　order　of　vibration　signal,　the　high-frequency　component　increases　gradually　and　the　low-frequency　component　decreases　gradually;　The　frequency　distribution　of　dynamic　stiffness,　impedance　and　dynamic　mass　of　the　structure　is　described　by　the　frequency　response　function　expression　of　different　signals;　Different　monitoring　signals　have　different　recognition　accuracy　for　high　and　low　frequency　components,　as　well　as　high　order　modal　recognition　accuracy　for　structures.　Vibration　acceleration　signal　monitoring　is　recommended　for　identification　of　high　order　frequency　components,　and　vibration　velocity　signal　monitoring　is　recommended　for　identification　of　low　order　frequency.　©　2018,　Editorial　Department　of　Transaction　of　Beijing　Institute　of　Technology.　All　right　reserved.