  Time-frequency analysis (TFA) techniques play an important role in the field
of machine fault diagnosis attributing to their superiority in dealing with
nonstationary signals. Synchroextracting transform (SET) and
transient-extracting transform (TET) are two newly emerging techniques that can
produce energy concentrated representation for nonstationary signals. However,
SET and TET are only suitable for processing harmonic signals and impulsive
signals, respectively. This poses a challenge for each of these two techniques
when a signal contains both harmonic and impulsive components. In this paper,
we propose a new TFA technique to solve this problem. The technique first
divides time-frequency (TF) coefficients into two types according to the chirp
rate of the signal, and then TF ridges are respectively extracted to prevent
the limitation for the independent use of SET and TET. This allows the
technique to generate an energy-concentrated TF representation for both
harmonics and impulses in the signal. Furthermore, we theoretically demonstrate
that the proposed technique retains the signal reconstruction capability. The
effectiveness of the proposed technique is verified using numerical and
real-world signals.
