MS Teams (please email amgrad@uwaterloo.ca for the meeting link)
Candidate
Nicholas RichardsonÌý| Applied Mathematics, University of À¶Ý®ÊÓƵ
Title
A Sparse Random Feature Model for Signal Decomposition
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Signal decomposition and multiscale signal analysis provide useful tools for time-frequency analysis. In this thesis, an overview of the signal decomposition problem is given and popular methods are discussed. A novel signal decomposition algorithm is presented: Sparse Random Mode Decomposition (SRMD). This method sparsely represents a signal as a sum of random windowed-sinusoidal features before clustering the time-frequency localized features into the constituent modes. SRMD outperforms state-of-the-art methods on a variety of mathematical signals, and is applied to real-world astronomical and musical examples. Finally, we discuss a neural network approach to tackle challenging musical signals.