A split spectrum processing (SSP) method is proposed to accurately determine the time-of-flight (ToF) of damage-scattered waves by comparing the instantaneous amplitude variation degree (IAVD) of a wave signal captured from a damage case with that from the benchmark. The fundamental symmetrical ($S_0$) mode in aluminum plates without and with a notch is assessed. The efficiency of the proposed SSP method and Hilbert transform in determining the ToF of damage-scattered $S_0$ mode is evaluated for damage identification when the wave signals are severely contaminated by noise. Broadband noise can overwhelm damage-scattered wave signals in the time domain, and the Hilbert transform is only competent for determining the ToF of damage-scattered $S_0$ mode in a noise-free condition. However, the calibrated IAVD of the captured wave signal is minimally affected by noise, and the proposed SSP method is capable of determining the ToF of damage-scattered $S_0$ mode accurately even though the captured wave signal is severely contaminated by broadband noise, leading to the successful identification of damage (within an error on the order of the damage size) using a triangulation algorithm.