This paper introduces a realization of Finite-length Impulse Response (FIR) filters with simultaneously variable bandwidth and Fractional Delay (FD). The realization makes use of impulse responses which are two-dimensional polynomials in the bandwidth and FD parameters. Unlike previous polynomial-based realizations, it utilizes the fact that a variable FD filter is typically much less complex than a variable-bandwidth filter. By separating the corresponding sub-filters in the overall realization, significant savings are thereby achieved. A design example, included in the paper, shows about 65 percent multiplication and addition savings compared to the previous polynomial-based realizations. Moreover, compared to a recently introduced alternative fast filter bank approach, the proposed method offers significantly smaller group delays and group delay errors.