With the rapid development of electronic information and computer science, the fast Fourier transform (FFT) has played an increasingly important role in digital signal processing (DSP). This paper presented a spectrum processing chiplet design method to solve slow speed, low precision, and low resource utilization in spectrum processing of general-purpose spectrum chips and field programmable gate array (FPGA). To realize signal processing, the Radix-2 4096-point FFT algorithm with pipeline structure is used to process spectral signals extracted from the time domain. To reduce the harm caused by spectrum leakage, a windowing module is added to optimize the input data, and the clock gating unit (CGU) is used to perform low-power management on the entire clock reset. The result shows the chiplet takes 0.368 ms to complete a 4096-point frequency sweep under a clock frequency of 61.44 MHz. The chiplet significantly improves speed and accuracy in spectrum processing, which has great application potential in wireless communication.