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The developments in the field of Very Large Scale Integration (VLSI) and rapid advances of Digital Signal Processing has laid the foundation for implementation of DSP algorithms using digital hardware such as Field Programmable Gate Array. The core function in every DSP system is of digital filtering and the preferred filter is FIR filters due to their advantages such as linear phase response, stability, less quantization noise and round-off noise. There is demand for miniaturization, high speed and low power dissipation in every application. In this work the optimization of FIR filter for these factors using different techniques is discussed. This book discusses that how the filter has been designed using the transposed structure using binary representation for the coefficients, then it is designed using the transposed structure with canonical signed digit (CSD) representation for coefficients and in the last filter has been designed using transposed structure with reduced addergraph (RAG) algorithm.