Fejer's theorem for Bundles

Question

Fej$\mathbf{\acute{e}}$r's Theorem For Bundles: Let $X$ be a compact space and $L\rightarrow X$ be a line bundle with metric, giving rise to a sphere bundle $\sigma :S\rightarrow X$. Let further $F\rightarrow X$ a bundle with metric.Then every $f\in \Gamma (\sigma^{*}F)$ has a Fourier coefficient $\hat{f}= \langle z^{k},f\rangle \in \Gamma (L^{-k}\otimes F)$, where $\hat{f}(x)= \frac{1}{2\pi i}\int _{S_{x}}(f_{x}\otimes z_{x}^{-k-1})dz_{x}$. Here $f_{x}$, $z_{x}$ denotes the restrictions of $f$ and $z$ to $S_{x}$. I can not understand how the integration is defined.