For front-end wireless application in small battery-powered devices, the discrete Fourier (DFT) transform is a critical processing method for discrete time signals. Advanced radix structures are created in an effort to reduce the impact of a transistor malfunction. To develop a DFT with radix sizes 4, 8, etc. is a complex and tricky issue for algorithm designers. The main reason for this is that the butterfly algorithm's lower radix level equations were manually estimated. This necessitates the selection of a new design process. As a result of fewer calculations and smaller memory requirements for computationally intensive scientific applications, this research focuses on the Radix-4 Fast Fourier Transform (FFT) technique. A new 64-point DFT method based on the Radix-4 FFT and a multi-stage strategy to solving DFT-related issues is presented in this paper. Based on the results of simulations with the Xilinx ISE, it can be concluded that the algorithm developed is faster than conventional approaches, with an 18.963ns delay and a power consumption of 12.68mW. Using the proposed FFT technique, this work also focuses on medical image compression for different tolerances. As a consequence of testing, it was discovered that the computed picture compression drop ratios of 0.10, 0.31, 0.61 and 0.83 had a direct relationship to the varied tolerances tested 0.0007625, 0.003246, 0.013075 and 0.03924. This makes medical image processing attractive. Fast reconstruction techniques, wireless medical devices, and other applications benefit from this FFT's low power consumption, little storage requirements, and high processing speed.