  Time-frequency representation (TFR) allowing for mode reconstruction plays a
significant role in interpreting and analyzing the nonstationary signal
constituted of various modes. However, it is difficult for most previous
methods to handle signal modes with closely-spaced or spectrally-overlapped
instantaneous frequencies (IFs) especially in adverse environments. To address
this issue, we propose an enhanced TFR and mode decomposition (ETFR-MD) method,
which is particularly adapted to represent and decompose multi-mode signals
with close or crossing IFs under low signal-to-noise ratio (SNR) conditions.
The emphasis of the proposed ETFR-MD is placed on accurate IF and instantaneous
amplitude (IA) extraction of each signal mode based on short-time Fourier
transform (STFT). First, we design an initial IF estimation method specifically
for the cases involving crossing IFs. Further, a low-complexity mode
enhancement scheme is proposed so that enhanced IFs better fit underlying IF
laws. Finally, the IA extraction from signal's STFT coefficients combined with
the enhanced IFs enables us to reconstruct each signal mode. In addition, we
derive mathematical expressions that reveal optimal window lengths and
separation interference of our method. The proposed ETFR-MD is compatible with
previous related methods, thus can be regarded as a step toward a more general
time-frequency representation and decomposition method. Experimental results
confirm the superior performance of the ETFR-MD when compared to a
state-of-the-art benchmark.
