• Ishwar Prasad Dehariya
• Hemant Amhia

Hilbert Transform faces several challenges in dealing with closely-spaced frequency components, short-time and weak disturbances, and interrelationships between two time-varying modes of nonlinear vibration due to its mixed mode problem associated with empirical mode decomposition (EMD). To address these challenges, analytical mode decomposition (AMD) based on Hilbert Transform is proposed and developed for an adaptive data analysis of both stationary and non-stationary responses. With a suite of predetermined bisecting frequencies, AMD can analytically extract the individual components of a structural response between any two bisecting frequencies and function like an adaptive bandpass filter that can deal with frequency-modulated responses with significant frequency overlapping. It is simple in concept, rigorous in mathematics, and reliable in signal processing.The Hilbert transform is a widely used transform in signal processing. In this thesis we explore its use for different applications: electrocardiography, modulation etc. The Hilbert- transform is a very popular method for spectral analysis for nonlinear and/or non-stationary processes. We examine its connection with the Hilbert transform and show limitations of the method. Lastly, the connection between the Hilbert transform and single-sideband modulation is investigated.

AMD, adaptive, EMD, Hilbert Transform, modulation, spectral.

"Implementation Of Hilbert Transform In Analytical Analysis", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 7, page no.394-398, July-2018, Available :http://www.jetir.org/papers/JETIR1807521.pdf

"Implementation Of Hilbert Transform In Analytical Analysis", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 7, page no. pp394-398, July-2018, Available at : http://www.jetir.org/papers/JETIR1807521.pdf