A class of linear-phase FIR filters for decimation, interpolation, and narrow-band filtering

A new class of linear phase finite impulse response (FIR) digital filters for decimation and interpolation is discussed. The transfer function of these filters is of the form H(z) = A (z
^D
) B(z)where D is the decimation or interpolation ratio and A (z
^D
) is realized at the lower sampling rate. The polynomial A (z
^D
) is adjusted so that the overall magnitude response presents an equiripple behavior in the pass-band, whereas B(z) provides an equiripple stopband response. An efficient iterative procedure for the design of the filters of this type is presented and the optimal selection of the orders of A(z
^D
) and B(z) is considered. Several examples show how the new decimators and interpolators require significantly fewer multiplications per second than equivalent conventional linear phase FIR and elliptic designs. The performance of these linear phase filters is about the same as that of the recursive filters of Martinez and Parks with only powers of z
^D
in the denominator. Some characteristics of the new filters, such as zero positions, coefficient sensitivity, and output noise variance due to roundoff errors, are discussed and compared with conventional FIR designs. Furthermore, it is shown that by cascading multistage new decimators and interpolators, we obtain efficient narrow-band filters requiring considerably fewer multiplications per output sample than equivalent elliptic designs.