Analytic unit quadrature signals with nonlinear phase

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Mono‐components for decomposition of signals (2006, methodology): “Sci. 2006; 29:1187–1198 In References [3,4] we establish the theory of non-linear Fourier atoms ei a(t), 06 t6 2 , where a is any complex number in D, and a is an absolutely continuous and strictly increasing function with a(2 )− a(0)=2 , and ′a(t) is the Poisson kernel for the unit disc at the poin”
On Instantaneous Frequency (2009, methodology): “The conditions were recently generalized by Qian et al.(34) But such discussions would be of very limited practical use in data analysis, for we cannot force our data to satisfy the conditions prescribed.”
Fourier spectrum characterization of Hardy spaces and applications (2008, background): “The relevant literature may be found in [1], [2], [3], [12], [4], [8], [13], [14], [15], [16] and their references.”
Characterization of Boundary Values of Functions in Hardy Spaces with Applications in Signal Analysis (2005, background): “with θ�a(t )= p|a|(t) > 0, where p|a| is the Poisson kernel of D at z = |a| (for more details see [ 11 ]).”