Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/33344
Title: Nonstationary Gabor Frames: Functions and Sequences
Authors: POH WEI SHAN, CHARLOTTE
Keywords: nonstationary, gabor, frames, functions, and, sequences
Issue Date: 19-Jan-2012
Source: POH WEI SHAN, CHARLOTTE (2012-01-19). Nonstationary Gabor Frames: Functions and Sequences. ScholarBank@NUS Repository.
Abstract: There are many methods for time-frequency analysis of signals, one of which uses standard Gabor analysis. However, Gabor frames have the limitation of fixed time-frequency resolution, which we try to overcome by extending the theory to nonstationary Gabor frames for square integrable functions and periodic sequences. Instead of using both modulation and translation of a single function to create a Gabor frame, we use a sequence of functions and only one of the operators to create the frame. After developing the theory for the frame that uses modulation, properties of the Fourier transform are used to obtain analogous results for the frame using translation. In addition, we also aim to find dual frames for the spaces of square integrable functions and periodic sequences. For applications, we use the theory for the sequence space and perform time-frequency analysis on signals and also reconstruct the signal with the theory we have for dual frames.
URI: http://scholarbank.nus.edu.sg/handle/10635/33344
Appears in Collections:Master's Theses (Open)

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