Fast Fourier Transform(FFT) processing is an important component of many Digital Signal Processing(DSP) and Communication Systems. In this book everything is so vividly presented from a basic concept to an advanced algorithm implementation. Particularly focused on mathematical analysis, algorithm implementation, high-level synthesis, and C/C++ prototyping. A new approach to design and implement FFT using radix-4^2 algorithm, and how the multidimensional index mapping reduces the complexity of FFT computation are proposed and discussed very clearly with required figures. Two approaches are given to implement the FFT algorithm, one is hardware(HDL) generation and the other is C/C++ prototyping. High-level synthesis has done by using Simulink and shown the reduced number of hardware in terms of multipliers and adder/ subtractors.