How to build ultra-fast floating-point FFTs in FPGAs

By Ray Andraka, Andraka Consulting Group
April 30, 2007 -- dspdesignline.com
    
Engineers targeting DSP to FPGAs have traditionally used fixed-point arithmetic, mainly because of the high cost associated with implementing floating-point arithmetic. That cost comes in the form of increased circuit complexity and often degraded maximum clock performance. Certain applications demand the dynamic range offered by floating-point hardware but require speeds and circuit sizes usually associated with fixed-point hardware. The fast Fourier transform (FFT) is one DSP building block that frequently requires floating-point dynamic range and high speed.

A textbook construction of a pipelined floating-point FFT engine capable of continuous input entails dozens of floating-point adders and multipliers. The complexity of these circuits quickly exceeds the resources available on a single FPGA. We fit the FFT design into a single FPGA without sacrificing speed or floating-point performance by using an alternative FFT algorithm and a hybrid of fixed- and floating-point hardware.

The resulting design has IEEE single-precision floating-point inputs and outputs that match the precision obtained with more conventional designs, yet is capable of as much as 1.2 gigasamples-per-second continuous data throughput and fits into one Xilinx Virtex-4 XC4VSX55 FPGA. The design performs 32-, 64-, 128-, 256-, 512-, 1,024-, or 2,048-point complex input Fourier transform, with size selected on the fly.

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