This paper is concerned with the sparse representation of analytic signal in Hardy space H2(D), where D is the open unit disk in the complex plane. In recent years, adaptive Fourier decomposition has attracted considerable attention in the area of signal analysis in H2(D). As a continuation of adaptive Fourier decomposition-related studies, this paper proves rapid decay properties of singular values of the dictionary. The rapid decay properties lay a foundation for applications of compressed sensing based on this dictionary. Through Hardy space decomposition, this program contributes to sparse representations of signals in the most commonly used function spaces, namely, the spaces of square integrable functions in various contexts. Numerical examples are given in which both compressed sensing and ℓ- minimization are used.