# Half-band filter

It follows from the filter's definition that its transition region, or skirt, can be centered at frequency  ${\displaystyle \scriptstyle f_{s}/4,}$  where  ${\displaystyle \scriptstyle f_{s}}$  is the input sample-rate. That makes it possible to design an FIR filter whose every other coefficient is zero, and whose non-zero coefficients are symmetrical about the center of the impulse response. (See Window design method)  Both of those properties can be used to improve efficiency of the implementation.[1][2]