Abstract: A complex adaptive Finite-Impulse-Response filter for processing complex digital data having real and imaginary data portions that includes a first data path for receiving and processing the real data portion of the complex input and a second data path for receiving and processing the imaginary data portion. Each first and second data path includes a corresponding plurality of adaptive weight circuits and accumulator circuits to perform respectively, multiplications of input data with a set of updatable coefficient data and accumulations of the multiplication results obtained. Two of multiplication results are obtained for each data path and a subset from each are accumulated to form a real output portion and imaginary output potion for the filter. A time delay circuit is provided to allow for proper time multiplexing of the imaginary output portion. The plurality of adaptive weight circuits have associated therewith first and secondary memory storage banks for storing the current coefficient data values.