  An analytical Green's function is developed to study the acoustic scattering
by a flat plate with a serrated edge. The scattered pressure is solved using
the Wiener-Hopf technique in conjunction with the adjoint technique. It is
shown that the kernel decomposition proposed in recent literature appears only
valid at high frequencies. We focus on this high-frequency regime and obtain
the scattered pressure in the form of a contour integral. We show that such an
integral, although complicated, can be evaluated exactly for any arbitrary
piecewise linear serrations, for which closed-form analytical Green's functions
are obtained. The derivation is validated by performing numerical integration
of the contour integral showing excellent agreement. The Green's function is
shown to agree well with the numerical results obtained using the finite
element method at high frequencies. The noise directivity patterns are studied
as a function of the frequency, serration amplitude, source position and Mach
number respectively. It is found that noise is often enhanced at low and may be
slightly reduced at high observer angles, which may be understood from the
perspective of an extended or removed rigid reflection surface. It is found
that increasing the mean-flow Mach number leads to increasingly evident noise
amplification at side angles, a seemingly strange Doppler behaviour exhibited
in source-fixed coordinate frames. The analytical Green's function is
applicable to both leading- and trailing-edge scatterings, and is particularly
suitable for developing a three-dimensional trailing-edge noise model that is
not only highly efficient but also capable of including non-frozen turbulence
effects.
