We present a new class of non-linear correlation filters that produce arbitrary quadratic decision surfaces. These new filters first linearly combine the output from other linear or non-linear filters using complex-valued weights. These linear combinations are then passed through a square- law function and again linearly combined to produce these decision surfaces. The linear correlation filters are designed separately form the non-linear fusion parameters. The output from this new algorithm is thresholded to allow tradeoffs between probability of detection and the probability of false alarms to be made. This algorithm is numerically very efficient as it reduces the number of correlation operations required. It is optically and electronically implementable.