Mathematics Colloquia and Seminars
PhD Exit Seminar: The Chirped Quilted Synchrosqueezing Transform and Its Application to Bioacoustic Signal AnalysisGGAM Colloquium
|Speaker:||Alex Berrian, UC Davis|
|Start time:||Fri, Mar 16 2018, 5:10PM|
In time-frequency analysis, a common problem is the retrieval of time-varying instantaneous frequency (IF) information from signals. Reassignment methods are often used for estimating IFs, as these methods circumvent the well-known Fourier uncertainty principle that limits linear transforms such as the short-time Fourier transform (STFT) and continuous wavelet transform. The synchrosqueezing transform (SST) has become a popular reassignment method due to its mathematically rigorous formulation and its formula for direct signal reconstruction from SST coefficients. However, the SST as originally formulated is ineffective when the IFs vary quickly. We construct a version of SST that accounts for fast IF variations using a quilted short-time Fourier transform (QSTFT), a signal-adaptive patchwork representation arising from STFTs computed with different window functions. We first build an analysis-resynthesis framework for QSTFT in depth that features perfect signal reconstruction from QSTFT coefficients. We then establish new theorems showing that using chirped windows enables the QSTFT and its respective SST (SST-QSTFT) to concentrate fast-varying IF information effectively. Finally, we apply the SST-QSTFT to numerical experiments on a dataset of animal call recordings as well as synthetic data, demonstrating its effectiveness for isolating precise IF information and its superior performance in the presence of noise.
Reception starts at 4:30 in 1147 MSB.