  Real-world phenomena that can be formulated as signals are often affected by
a number of factors and appear as multi-component modes. To understand and
process such phenomena, "divide-and-conquer" is probably the most common
strategy to address the problem. In other words, the captured signal is
decomposed into signal components for each individual component to be
processed. Unfortunately, for signals that are superimposition of
non-stationary amplitude-frequency modulated (AM-FM) components, the
"divide-and-conquer" strategy is bound to fail, since there is no way to be
sure that the decomposed components take on the AM-FM formulations which are
necessary for the extraction of their instantaneous frequencies (IFs) and
amplitudes (IAs). In this paper, we propose an adaptive signal separation
operation (ASSO) for effective and accurate separation of a single-channel
blind-source multi-component signal, via introducing a time-varying parameter
that adapts locally to IFs and using linear chirp (linear frequency modulation)
signals to approximate components at each time instant. We derive more accurate
component recovery formulae based on the linear chirp signal local
approximation. In addition, a recovery scheme, together with a ridge detection
method, is also proposed to extract the signal components one by one, and the
time-varying parameter is updated for each component. The proposed method is
suitable for engineering implementation, being capable of separating
complicated signals into their components or sub-signals and reconstructing the
signal trend directly. Numerical experiments on synthetic and real-world
signals are presented to demonstrate our improvement over the previous
attempts.
