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The talk will introduce AFD of functions in Hardy spaces into mono-components that by definition are functions in the Hardy space possessing positive analytic instantaneous frequency.Fourier series and Fourier transform are particular examples of mono-component decomposition.The adaptivity addresses fast decomposition in energy.The talk will briefly mention the relations between AFD and TM system,the open question on best approximation by rational functions of given order,the construction of backward shift invariant subspace in terms of Beurling-Lax Theorem,etc.