Design and implementation in VHDL code of the two-dimensional fast Fourier transform for frequency filtering, convolution and correlation operations

Abstract

The two-dimensional Fast Fourier Transform (FFT 2D) is an essential tool in the two-dimensional discrete signals analysis and processing, which allows developing a large number of applications. This article shows the description and synthesis in VHDL code of the FFT 2D with fixed point binary representation using the programming tool Simulink HDL Coder of Matlab; showing a quick and easy way to handle overflow, underflow and the creation registers, adders and multipliers of complex data in VHDL and as well as the generation of test bench for verification of the codes generated in the ModelSim tool. The main objective of development of the hardware architecture of the FFT 2D focuses on the subsequent completion of the following operations applied to images: frequency filtering, convolution and correlation. The description and synthesis of the hardware architecture uses the XC3S1200E family Spartan 3E FPGA from Xilinx Manufacturer.