An　interval-sweeping　pulse　equivalent　sampling　(ISPES)　method　based　on　compressed　sensing　technique　is　proposed　to　enhance　the　frequency　response　of　phase-sensitive　optical　time-domain　reflectometry　(phi-OTDR).　The　proposed　method　achieves　an　equivalent　high-sampling-rate　acquisition　of　Rayleigh　backscattered　signals　along　each　sensing　point　of　the　fiber　by　the　interval-sweeping　pulse　sampling　and　compressed　sensing　reconstruction.　Meanwhile,　based　on　the　Whittaker-Shannon　interpolation　formula,　the　observation　matrix　corresponding　to　the　interval-sweeping　pulse　sampling　is　successfully　constructed　and　proved,　which　is　easy　to　implement　in　hardware.　In　experiments,　an　ultrasonic　signal　with　a　frequency　up　to　28　kHz　at　the　end　of　a　4.4-km　sensing　fiber　is　accurately　identified　by　using　this　method,　which　outperforms　other　compressed-sensing-based　methods.　And　multi-frequency　vibration　signals　are　also　accurately　detected.　Besides,　this　method　performs　signal　compression　while　sampling.　The　number　of　samples　is　only　13.3%　of　the　reconstructed　data,　significantly　reducing　the　amount　of　data　acquisition/transmission/storage.　Therefore,　the　proposed　method　can　effectively　enhance　the　frequency　response　of　phi-OTDR　to　sparse-wideband　vibration　signals　without　any　hardware　modification.　It　also　has　great　advantages　in　reducing　the　hardware　burden　and　improving　the　response　speed.