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We propose a unification of recent advances (Renyi DP, privacy profiles, $f$-DP and the PLD formalism) via the \\emph{characteristic function} ($\\phi$-function) of a certain \\emph{dominating} privacy loss random variable. We show that our approach allows \\emph{natural} adaptive composition like Renyi DP, provides \\emph{exactly tight} privacy accounting like PLD, and can be (often \\emph{losslessly}) converted to privacy profile and $f$-DP, thus providing $(\\epsilon,\\delta)$-DP guarantees and interpretable tradeoff functions. Algorithmically, we propose an \\emph{analytical Fourier accountant} that represents the \\emph{complex} logarithm of $\\phi$-functions symbolically and uses Gaussian quadrature for numerical computation. 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