In this paper a recursive finite impulse response filter based on the linear least squares estimation algorithm with fixed regression window length is presented. The recursive execution achieves a significant reduction in the computational effort for larger regression window lengths, while at the same time keeping the calculation latency very low and constant. This predestines the presented implementation for fast online filtering of the measurement signal and estimating its first derivative in several application areas in power electronics and electrical drives. Hardware realization of the presented algorithm on an FPGA using fixed-point arithmetic and a comparison with non-recursive moving least squares estimator variants proves the superiority of the proposed algorithm.