Instantaneous frequency was introduced to describe the dependency of frequency components on time for non-stationary signals. A powerful alternative to the Fourier-based spectral analysis that provides insufficient resolution for the temporal progression of all frequency components, the concept of instantaneous frequency has rarely been applied to machine monitoring and diagnosis. The confusing fact that instantaneous frequencies determined could occasionally be negative and the associated amplitudes could be infinite for certain types of vibration signals inevitably limits the adaptability of the concept to fault detection as a result. Significant insight into the applicability of instantaneous frequency is gained through re-examining the fundamentals upon which the concept was first defined. It is found that the Hilbert-transform-based definition of instantaneous frequency is applicable only to signals of monocomponent, thus implying the need for separating a multicomponent signal into its monocomponent subsets. Misuse of the definition to multicomponent signals would result in the individual instantaneous frequency associated with each inherent monocomponent being averaged and thus obscure the underlying characteristics of the signal. A mathematically complete decomposition scheme effective in resolving a multicomponent signal into an orthogonal space spanned by its intrinsic monocomponents is explored. Several examples are considered to show that the scheme not just enables the removal of the difficulties commonly encountered in applying instantaneous frequency but also imparts valid renditions to the interpretation of fault-induced bifurcation and dynamic instability.