This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a piecewise linear periodic leading edge. The Wiener-Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to allow analytical progress. A fully analytic solution is obtained in terms of a modal expansion for the far-field noise which is obtained by summing only a finite number of cuton modes, allowing very quick evaluation. The analytic solution is compared to experimental results for five test case leading-edge geometries. Good agreement is seen indicating the analytic model is capturing the key features of the interaction such as the destructive interference from the tip and root. In four of the five test cases the serrated edges show large reductions of noise compared to the straight edge at mid and high frequencies, however the square wave geometry is seen to be ineffective at noise reduction for high frequencies.