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The properties of a general class of monopulse antenna difference patterns which are obtained by differentiating a desirable class of antenna sum patterns are analyzed. Their corresponding aperture distributions are synthesized using the Fourier transform. It is found that of the general class of patterns considered, there is one family which gives the best compromise between slope at boresight and sidelobe level. Curves are presented which relate sidelobe level and slope at boresight for this particular family; these curves may be used to design monopulse difference patterns for either a specified slope at boresight or a specified sidelobe level. Simple expressions for the corresponding far-field difference patterns, their beamwidth, and their aperture distributions are given.