In the past, several different approaches to Synthetic Discriminant Function (SDF) filter design have been proposed. These include: conventional SDFs which control the correlation values at the origin, Minimum Variance SDFs (MVSDFs) which minimize the noise sensitivity of the filters, Minimum Average Correlation Energy (MACE) filters which maximize the peak sharpness, and Linear Phase Coefficient Composite (LPCC) filters which use phasor addition and subtraction for inherent class discrimination. In this paper, we introduce a new family of SDF filters of which all the above are special cases. Each filter in this family is characterized by two parameters (alpha) 1 and (alpha) 2. Various choices of ((alpha) 1,(alpha) 2) lead to above special filters. For example, (alpha) 1 equals 1 and (alpha) 2 equals 0 leads to MACE LPCC filters which are hybrid versions of MACE and LPCC filters. This family of filters is evaluated using the Minimum Probability of Error (MPE) criterion and a data base of aircraft images. These simulation experiments confirm the superior performance of this filter family. Also, we observe the interesting result that the MPE is at its lowest not for one of the four special filters listed above, but for a combination of them.