Adjustable fractional-delay FIR filters using the farrow structure and multirate techniques

The Farrow structure can be used for efficient realization of adjustable fractional-delay finite-length impulse response (FIR) filters, but, nevertheless, its implementation complexity grows rapidly as the bandwidth approaches the full bandwidth. To reduce the complexity, a multirate approach can be used. In this approach, the input signal is first interpolated by a factor of two via the use of a fixed half-band linear-phase FIR filter. Then, the actual fractional-delay filtering takes place. Finally, the so generated signal is downsampled to retain the original input/output sampling rate. In this way, the bandwidth of the fractional-delay filter used is halved compared to the overall bandwidth. Because the complexity of halfband linear-phase FIR filter interpolators is low, the overall complexity can be reduced. In this paper, we present more implementation details, design trade-offs, and comparisons when the filters are implemented using multiple constant multiplication techniques, which realize a number of constant multiplications with a minimum number of adders and subtracters.