A processor includes a decode unit to decode a packed finite impulse response (FIR) filter instruction that indicates one or more source packed data operands, a plurality of FIR filter coefficients, and a destination storage location. The source operand(s) include a first number of data elements and a second number of additional data elements. The second number is one less than a number of FIR filter taps. An execution unit, in response to the packed FIR filter instruction being decoded, is to store a result packed data operand. The result packed data operand includes the first number of FIR filtered data elements that each is to be based on a combination of products of the plurality of FIR filter coefficients and a different corresponding set of data elements from the one or more source packed data operands, which is equal in number to the number of FIR filter taps.