Realization of Root Raised Cosine Roll-Off Filters Using a Recursive FIR Filter Structure

Root raised cosine roll-off (RRC) filter is one of the most fundamental elements in modern digital communications. This paper proposes a new method to efficiently realize the RRC filter. The method employs cubic Hermite interpolation to obtain a piecewise-polynomial approximation for the impulse response of the RRC filter. Then, the approximated impulse response is efficiently realized by using a transversal filter with a very small number of taps followed by integrators with a simple recursive structure, named cascaded recursive finite impulse response (CR-FIR) filter. As an example, an RRC filter with roll-off factor 0.5 is constructed by using the CR-FIR filter with only nine multipliers. Performance of the RRC filter in matched filtering is examined by computer simulations. Then, it is shown that the constructed RRC matched filter has nearly the same performance as the ideal filter.