We have addressed the problem of automated detection of biological macromolecules from electron micrographs by designing a detection filter which combines conventional correlation technique with a synthetic discriminant function (SDF) in conjunction with the constraint to minimize the energy in the correlation plane and that of noise. Combining the constrained SDF filter with circular harmonic expansion results in rotational invariance of the detection process. We define measures to evaluate filter performance by test calculations and discuss the choice of parameters for filter development. Compared with the conventional matched filter, improved recognition and discrimination of objects to be detected is achieved. Applications of the filter to detect biological macromolecules in electron micrographs are presented, demonstrating the improvements in object detection as well as the limitations of the method.