Design of narrow-band FIR bandpass digital filters with reduced arithmetic complexity

A computationally efficient realization of a symmetrical bandpass FIR filter is derived. The realization is composed of two branches, each consisting of a cascade of two FIR sections. In each branch, the first FIR section has a sparse impulse response with only every
L
th sample being nonzero. The second section generates the remaining samples via interpolation. The method is applicable to both linear and nonlinear phase cases. Approximate expressions for the optimal value of
L
and the corresponding number of multipliers and adders required in the overall realization are derived. In narrow-band implementations, the number of multipliers and adders is approximately proportional to
1/\sqrt{{\Delta}F}
, where
{\Delta}F
is the desired relative transition bandwidth. Typically, the required number of multipliers and adders is
1/2
to
1/4
th of those in the conventional linear or nonlinear phase direct-form implementations. The total number of delays is only slightly larger than that required in the conventional implementations. The structure allows simple tuning of the center frequency of the bandpass filter and has good finite wordlength properties.