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This paper presents an analysis of radiation from a horn with a superquadric aperture, modeled using a cascade of superquadric waveguides. Electromagnetic fields within each waveguide are expressed in terms of a set of orthogonal modes derived from polynomial functions based on a Cartesian coordinate system. The scattering matrix at the horn aperture is obtained by calculating the scattering matrix at each of the waveguide junctions using mode matching, and cascading them appropriately. Radiation patterns corresponding to both x- and y-polarizations of the input excitation are then obtained by integrating the aperture field. The computed numerical results are validated by comparing them with the corresponding results obtained from measurements.