This paper presents an analytic solution for aerodynamic noise generated by an unsteady wall pressure gust interacting with a spanwise variable trailing edge in a background steady uniform ow. Viscous and non-linear e ects are neglected. The Wiener- Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to permit analytical progress. The solution is obtained in terms of a tailored modal expansion in the spanwise coordinate, however only nitely many modes are cuton, therefore the far- eld noise can be quickly evaluated. The solution gives insight into the potential mechanisms behind the reduction of noise for plates with serrated trailing edges compared to those with straight edges. The two mechanisms behind the noise reduction are an increased destructive interference in the far eld, and a redistribution of acoustic energy from low cuton modes to higher cuto modes. Five di erent test case trailing-edge geometries are considered. The analytic solution identi- es which geometries are most e ective in di erent frequency ranges; geometries which promote destructive interference are best at low frequencies, whilst geometries which promote a redistribution of energy are better at high frequencies.