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Compact objects are natural laboratories to test fundamental physics in extreme conditions. Our knowledge of them grows dramatically with the improvement of new theoretical models, observational instruments, analysis techniques, and computing power. For example, the simultaneous observations made with NICER and ground-based radio telescope allow us to detect the X-ray enhancement during the giant radio pulse in Crab pulsar. Furthermore, advanced and automated algorithms are needed in exploring hidden physics and searching for new objects as new data formats are born and a huge amount of data is accumulated. I will introduce my recent works on developing and applications of time-frequency analysis algorithms, including a systematic search for ultraluminous X-ray pulsars that challenges the current understandings of magnetospheric accretion onto neutron stars, and a study of time-frequency properties of gravitational wave signals from both coalescence of compact objects and core-collapse supernovae. Finally, I will introduce an X-ray CubeSat project that aims for continuous gravitational waves from compact objects, follow-up observations of transient events, and non-stationary phenomena around super-massive black holes.