 Specifically, if the region of support for the filter is assumed to be rectangular and centered at the origin, we have

formula_70

formula_71

Using the above equation to implement an FIR filter requires roughly one-half the number of multiplications of an implementation, although both implementations require the same number of additions and the same amount of storage.If the impulse response of an FIR filter possess other symmetries, they can be exploited in a similar fashion to reduce further the number of required multiplications.The FIR filter can also be implemented by means of the Discrete Fourier transform (DFT).