Abstract / truncated to 115 words (read the full abstract)

In this dissertation, the traditional Gabor represantation with sinusoidal basis functions, which is widely used in the time-frequency analysis of non-stationary signals, is extended to the Fractional Gabor expansion with fractionally modulated basis functions. The completeness and biorthoganility conditions of the analysis and synthesis basis sets of the expansion are derived. Then, a discrete fractional Gabor expansion, that can be used to analyze discrete-time signals, is obtained by sampling the continuous-time represantation. By deriving the completeness and biorthoganility conditions, the discrete fractional Gabor expansion can be implemented on a computer to analyze discrete-time signals. Furthermore, to increase the time-frequency resolution of the signal represantation, time-scaled version of a mother window are used to obtain Multi-window ... toggle 3 keywords

time-frequency analysis – gabor expansion – fractional fourier transform

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