In the past, several different approaches to synthetic discriminant function (SDF) filter design have been proposed, including 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 are obtained as the sum of training images weighted by linear phase coefficients. 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 α1 and α2. Various choices of (α1 , α2) lead to the above special filters. For example, α1 = 1 and α2 = 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 database 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.