The design of the physical layer (PHY) of Long Term Evolution (LTE) standard is heavily influenced by the requirements for higher data transmission rate, greater spectral efficiency, and higher channel bandwidths. To fulfill these requirements, orthogonal frequency division multiplex (OFDM) was selected as the modulation scheme at the PHY layer. The discrete Fourier transform (DFT) and the inverse discrete Fourier transform (IDFT) are fundamental building blocks of an OFDM system. Fast Fourier transform (FFT) is an efficient implementation of DFT. This thesis focuses on a novel high-throughput hardware architecture for FFT computation utilized in wireless communication systems, particularly in the LTE standard. We implement a fully-pipelined FFT architecture that requires fewer number of computations. Particularly, we discuss a novel approach to implement FFT using the combined Good-Thomas and Winograd algorithms. It is found that the combined Good-Thomas and Winograd FFT algorithms provides a significantly more efficient FFT solution for a wide range of applications. A detailed analysis and comparison between different FFT algorithms and potential architectures suitable for the requirements of the LTE standard is presented. Theoretical results have been validated by the implementation of the proposed approach on a field-programmable gate array (FPGA). As demonstrated by the mathematical analysis, a significant reduction has been achieved in all the design parameters, such as computational delay and the number of arithmetic operations as compared to conventional FFT architectures currently used in various wireless communication standards. It is concluded that the proposed algorithm and its hardware architecture can be efficiently used as an enhanced alternative in the LTE wireless communication systems.