We present a methodology for implementing NGD using a Finite Impulse Response (FIR) filter. The NGD concept is counter-intuitive in nature, so we first provide the basic theory of FIR-based NGD system synthesis based on second-order FIR systems. We include synthesis results that prove the viability of using FIR filters for NGD functions under specific conditions. We then design, simulate and test FIR-based NGD parameters before building an FPGA-based proof-of-concept implementation for embedded systems. The experimental results show how the frequency responses of the NGD function at baseband frequency correlate well with the theoretical hypothesis, supporting our analysis and validating our methodology.