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Zero frequency filtering is a technique used in the characterization and analysis of glottal activity from speech signals. The filter design originally proposed has an infinite impulse response (IIR) filter followed by two successive finite impulse response (FIR) filters. In this paper, the process of its computation is analyzed and a simplified FIR implementation is proposed by employing the inherent pole-zero cancellation involved in the process. Theoretical proofs are derived in both, frequency and time domains. We show that the theoretically derived FIR filter is a convolution of two filters, whose impulse responses are triangular shaped. The advantage of the proposed FIR filter lies in reduction of computational requirements for zero frequency filtering which include - 1) use of single-precision floating point and 2) stability of the filter.