Abstract: A finite impulse response filter that has the ability to use arbitrary TAPs that are essentially random access TAPs includes a plurality of circuits. The samples it operates on do not need to be a contiguous form. A sequencer is provided for counting up to a programmable number each time a start pulse is encountered and to provide an address and an incrementing address to a delta RAM, a coefficient RAM, and a micro code RAM. The delta RAM is used for storing the number of the TAP that is to be accessed. Delta Adders that directly follow the delta RAM are used with an input counter for making a ring counter for the input samples. A first and second sample RAM are used to hold incoming samples. An adder circuit is used for adding the output of the two sample RAMs to provide an output signal. A multiplier accumulator is connected to the adder circuit for receiving the output signal. The sequencer provides all the timing for the different cycles of the multiplier accumulator.