الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Hilbert-Huang transform (HHT) was first introduced in 1998 as an adaptive time-frequency transform suitable for non-linear and non-stationary signals. HHT consists oftwo steps: first, the Empirical Mode Decomposition (EMD), second, the Hilbert Spectrum. EMD adaptively decomposes the signal into Intrinsic Mode Functions (IMFs), which are signals having a meaningful Hilbert Transform (HT). Since its introduction, HHT was applied to different problems in several fields of science and engineering. Driven by the needs of the different applications, many modifications and improvements were suggested to HHT. In this thesis, we worked on enhancing the performance of HHT by developing an improved algorithm for EMD. EMD was found to behave like a dyadic filter bank when operating on a broadband signal. This means that the frequency content of the IMFs decreases from one IMF to the following. A signal with lower frequency contents can be represented with fewer points than one with a higher frequency content. Our proposed method, the Computationally Adaptive Empirical Mode Decomposition (CAEMD) uses this property to reduce the calculation required. It works by approximating the data by a Piecewise-Cubic polynomial (PCP). Using mathematical operations on the generated PCP, the CAEMD algorithms proceeds generating IMFs which can be identical to the that generated by the EMD . Results have shown that CAEMD improves execution time and reduces the required storage for the IMFs when compared with EMD. We also proposed a method to calculate the Hilbert transform of a cubic spline, which is compatible with the results obtained from CAEMD. Our method is capable of efficiently calculating the Hilbert Transform of cubic splines. Our proposed approach rewrites the cubic spline and reorders calculations needed to calculate Hilbert transform of a spline to increase the temporal locality of repetitive tasks. Then, it creates lookup tables of these values instead of reevaluating them. We validated this method against functions with known Hilbert transform and demonstrated its execution time efficiency. Finally, we suggested a speech feature extraction method based on HHT and tested it in speech recognition. Mel Hilbert Frequency Cepstral Coefficients (MHFCCs) use Hilbert Huang Transform (HHT) instead of the windowing and Fourier transform scheme used in Mel Frequency Cepstral Coefficients (MFCCs), which are the commonly used features. By using HHT, we no longer have to assume the stationarity of the signal and we can obtain its instantaneous frequency. HHT is capable of obtaining a high frequency resolution representation of the signal regardless of the size of the time window used. Results have demonstrated that MHFCCs outperform MFCCs in recognition accuracy for small time windows.