Implementation of Linear-Phase FIR Filters for a Rational Sampling-Rate Conversion Utilizing the Coefficient Symmetry

This paper proposes an efficient structure for implementing a linear-phase finite-impulse-response (FIR) filter of an arbitrary order
$N$
for the sampling-rate conversion by a rational factor of
$L/M$
, where
$L(M)$
is the integer upsampling (downsampling) factor to be performed before (after) the actual filter. In this implementation, the coefficient symmetry of the linear-phase filter is exploited as much as possible and the number of delay elements is kept as low as possible while utilizing the following facts. When increasing (decreasing) the sampling rate by a factor of
$L(M)$
, only every
$L$
th input sample has a nonzero value (only every
$M$
th output sample has to be evaluated). In this way, the number of required multiplications per output sample is reduced approximately by a factor of two compared with the conventional polyphase implementation. The proposed implementation is first illustrated using two examples. Based on these examples, guidelines are then given on how to efficiently realize an
$N$
th-order linear-phase FIR filter for a sampling-rate converter having an arbitrary rational conversion factor
$L/M$
. Finally, the implementation complexity of the proposed approach is evaluated and some examples are included, showing the efficiency of the proposed implementation compared with other existing ones.