Radix-2, radix-4, and radix-2^k are some variations of the Fast Fourier Transform (FFT) algorithm, which is used to calculate the Discrete Fourier Transform (DFT) of a sequence. Among these, the radix-2^k algorithm is particularly noteworthy because of its low-power requirements, versatility, and straightforward control logic. To provide a simplified butterfly unit with low memory requirement, the suggested radix-2^k architecture uses a Multiple Delay Commutator (MDC). Data shifting along the delay line is controlled by an input scheduling algorithm, which also helps to reduce power usage. To support high-speed applications, this work proposes a radix-2² FFT design with a Vedic multiplier. The design is implemented on a Xilinx Virtex-5 FPGA board for 8-point, 16-point, 512-point, and 1024-point FFTs. In particular, the 1024-point Radix-2² FFT architecture uses 121 registers, 11,629 LUTs, and 5,515 slices to achieve a delay of 42.102 ns integration of a Vedic multiplier within the butterfly unit resulted in improved operational performance and reduction in area.