Shrew Distributed Denial-of-Service (DDoS) attacks are stealthy, concealing their malicious activities in normal traffic. Although it is difficult to detect shrew DDoS attacks in the time domain, the existent energy exposes them in frequency domain. For this purpose, online Power Spectral Density (PSD) analysis necessitates real-time PSD data conversion. In this paper, an optimized FPGA based accelerator for real-time PSD conversion is proposed, which is based on our innovative component-reusable Auto-Correlation (AC) algorithm and the adapted 2N-point real-valued Discrete Fourier Transform (DFT) algorithm. Further optimization is achieved through the exploration of algorithm characteristics and hardware parallelism for this case. Evaluation results from both simulation and synthesis are provided. The overall design can be easily placed in a Xilinx Virtex2 Pro FGPA.