| Abstract: |
| Real-world signals, such as those from mechanical systems or medical data, are typically non-stationary and composed of multiple time-varying components. Traditional methods often struggle with mathematical rigor or lack the flexibility needed for dynamic environments.
This talk presents advanced mathematical frameworks for the high-resolution analysis and recovery of these multi-component signals. First, we discuss the Adaptive Synchrosqueezing Transform (SST), which improves upon standard wavelet- and STFT-based SST by adaptively selecting time-varying parameters to resolve blurry time-frequency representations. Second, we address the challenge of signals with crossover instantaneous frequencies-a scenario where traditional well-separated conditions fail. We introduce a Chirplet Transform-based approach and a mathematically rigorous Signal Separation Operator that acts as an overpass in the time-frequency plane to resolve intersecting components.
Finally, we present robust performance of these methods across machinery fault diagnosis, social media depression screening, and radar signal classification; these advancements further form a rigorous, adaptive framework for non-stationary signal separation, whose integration with deep learning delivers high performance across these key engineering and data science domains. |
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