Mathematics Colloquia and Seminars

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In the field of signal processing, one frequently seeks to model a signal with time-varying oscillatory properties as a sum of distinct (unknown) amplitude-phase components describing instantaneous amplitudes (IAs) and instantaneous frequencies (IFs). One may use a time-frequency representation such as the continuous wavelet transform (CWT) or the short time Fourier transform (STFT) to analyze the signal. However, these transforms provide blurry amplitude and frequency information, thereby complicating the task of accurately determining each amplitude-phase component. Hence, one needs a post-processing method to sharpen the blurry signal information. The tool of interest to us is the Synchrosqueezing transform (SST), which sharpens the picture of IAs and IFs provided by the CWT or STFT, and enables the reconstruction of each separate amplitude-phase component for a certain class of signals. We propose adapting the SST technique for larger classes of signals by formulating the SST in the context of adaptive time-frequency representations, including the nonstationary Gabor transform and the Chirplet transform. We'll conclude by proposing some audio-related applications. Joint work with Naoki Saito.