The deployment of a low-power broadband acoustic spectrum analyzer in the ocean is of great interest, particularly for underwater monitoring applications. This paper presents a real-time spectrum analyzer on a Field Programmable Gate Array. The hardware complexity is reduced using a Hann window with a 50% overlap at the input of the Fast Fourier Transform algorithm. Also, using a logarithmic scale, the frequency range represented is equal to 32,536 Hz. The design is demonstrated using Xilinx\'s Artix 7 System-on-Chip. To verify the accuracy of the implemented circuit, it is compared against the performance of an ideal simulated circuit in Matlab.