Daubechies, IngridWu, Hau-TiengChen, Ziyu2021-09-142021-09-142021https://hdl.handle.net/10161/23789<p>This dissertation introduces algorithms that analyze oscillatory signals adaptively. It consists of three chapters. The first chapter reviews the adaptive time-frequency analysis of 1-dimensional signals. It introduces models that capture the time-varying behavior of oscillatory signals. Then it explains two state-of-the-art algorithms, named the SynchroSqueezed Transform (SST) and the Concentration of Frequency and Time (ConceFT), that extract the instantaneous information of signals; this chapter ends with a discussion of some of the shortcomings of SST and ConceFT, which will be remedied by the new methods introduced in the remainder of this thesis. The second chapter introduces the Ramanujan DeShape Algorithm (RDS); it incorporates the periodicity transform to extract adaptively the fundamental frequency of a non-harmonic signal. The third part proposes an algorithm that rotates the time-frequency content of an oscillatory signal to obtain a time-frequency representation that has fewer artifacts. Numerical results illustrate the theoretical analysis.</p>MathematicsApplied mathematicsApplied harmonic analysisSignal processingTime-frequency analysisDissertation