A signal decomposition or lowpass filtering with Hilbert transform?

Recently, Chen and Wang discovered an explicit formula that makes use of the Hilbert transform for accurate decomposition of a lower harmonic from a signal composition. This letter presents another proof with a new interpretation for the formula using the Bedrosian identity for overlapping signals. This new and simpler proof is based only on the Hilbert transform and does not involve presentation of the Fourier transform. As a result the discovered formula is introduced as a lowpass filter suitable for non-stationary signals.