The Bedrosian identity has considerable importance for the nonlinear and non-stationary signal processing. In this paper we develop a unified mathematical treatment for Bedrosian identity. In order to study the Bedrosian identity of real-valued functions, we turn to study the equation F(z)G(z) = H(z), where G(z) and H(z) are both analytic functions belonging to Hardy spaces. Either the function F(z) is a meromorphic function, in this case its poles are relative to the zeros of G(z); or F(z) is a holomorphic function, but it doesn't belong to any Hardy space. It is shown that the theorem established by this new approach includes many existing results as its special cases.
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