A method and apparatus for performing complex digital filters. According to one aspect of the invention, a computer system generally having a transmitting unit, a processor, and a storage device is described. The storage device is coupled to the processor and has stored therein a routine. When executed by the processor, the routine causes the processor to perform a digital filter on unfiltered data items using complex coefficients to generate an output data stream. Execution of the routine causes the processor to perform outer and inner loops. The outer loop steps through corresponding relationships between the complex coefficients and the unfiltered data items. Each of these corresponding relationships is used by the digital filter to generate the output data stream. The inner loop steps the complex coefficients. Within the inner loop, the unfiltered data item corresponding to the current complex coefficient is determined according to the current corresponding relationship. Then, in response to receiving an instruction, eight data elements are read and used to generate a currently calculated complex number. As a result of the manner in which these eight data elements are stored, the currently calculated complex number represents the product of the current complex coefficient and its corresponding unfiltered data item. The currently calculated complex number is then added to the current output packed data. As a result, the current output packed data stores the sum of the complex numbers generated in the current inner loop.