The Fourier expansion of a boolean function $f : \{-1,1\}^n \to \{-1,1\}$ is simply its representation as a real, multilinear polynomial. (Multilinear means that no variable $x_i$ appears squared, cubed, etc.) For example, suppose $n = 2$ and $f = {\textstyle \min_2}$, the “minimum” function on $2$ bits:

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