Finite Impulse Response (FIR) filtering operation can be expressed as Multiplication of vectors by scalars. A high speed design for FIR filters based on a Computation SHaring Multiplier (CSHM) is presented here. This CSHM, which specially targets computation reuse in vector-scalar products. The authors’ recently proposed Computation SHaring Multiplication (CSHM) approach can be effectively used to reduce redundant computations in FIR filtering operation. The paper is to represent the multiplication in FIR filtering operation as a combination of add and shift operations over the common computation results.