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ECE 734: Project Presentation. 64-point FFT Algorithm for OFDM Applications using 8-point DFT processor (radix-8). Pankhuri May 8, 2013. Fast Fourier Transform. Uses symmetry and periodicity properties of DFT to lower computation 64-point DFT computes a sequence X(f),

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ece 734 project presentation
ECE 734: Project Presentation

64-point FFT Algorithmfor OFDM Applications using 8-point DFT processor (radix-8)


May 8, 2013

fast fourier transform
Fast Fourier Transform
  • Uses symmetry and periodicity properties of DFT to lower computation
  • 64-point DFT computes a sequence X(f),
  • Basis of FFT: DFT can be divided into smaller DFTs.
  • e.g. radix-8 algorithm divides FFT into 8-point DFTs, radix-2: 2-point DFTs (BF)
8 point fft processor details
8-point FFT processor details
  • FFT8 processor uses Winograd algorithm
  • Minimizes multiplication (more expensive operation) at expense of increased additions and some more memory requirement.
  • FFT8 (unit that performs base FFT operation) is pipelined
  • One complex number is read from/written into input/output data buffer each clock cycle. (Total of 14 clock cycles)
  • Supports clock frequency of up to 250 MHz
8 point fft processor algorithm
8-point FFT processor algorithm

8 – point Winograd FFT

processor design overview
Processor Design Overview

Buffer RAM1

Twiddle factor multiplier

8-point FFT unit 1

Complex Input

  • Synthesis and Simulation: Altera Quartus II
  • Language: Verilog
  • Target: Stratix IV FPGA

8-point FFT unit 2

Buffer RAM2

Buffer RAM3

Complex Output

processor design overview1
Processor Design Overview
  • Data buffers: convert data from 8-inverse order to natural order e.g. without third buffer at the end, the output order is 0,8,16….56, 1,9,17,….. (8-inverse order).
  • Use altsyncram, can store 2x64 complex data
  • One bank is written to from previous stage, other can be read simultaneously.
  • FFT Blocks: Only constant multiplications needed are 1/√2 (bunch of shift and add operations)
processor design overview2
Processor Design Overview
  • Sixteen 8-point FFT units are avoided here by instead multiplexing the use of two units at expense of increased latency.
  • Twiddle factor multiplier is a ROM having pre-calculated twiddle factors
  • Complex multiplication is accomplished by breaking it into three multiplies and five additions. (lpm_mult mega function)

(A + jB)(C + jD) = C(A-B) + B(C-D) + j(A(C-D) – C(A-B))

learning outcomes
Learning Outcomes
  • Details of various implementation issues of FFT processor design - resolving bandwidth issues when multiple stages are involved, reducing multiplier count (pipelining), total number of multiplications required (algorithm efficiency)
  • Read about a LOT of FFT algorithms used for OFDM applications (before shortlisting this one). Various strategies to reduce computation employed in these algorithms especially popularity of radix-8 algorithms over radix-2.
future work applications
Future Work & Applications
  • Future Work: Modular design allows it to be used together with other 64-point FFTs to create larger size. (Much as this design is built using 8-point units)
  • Structure can be configured in Xilinx, Altera, Alcatel, Lattice FPGA devices and ASIC
  • Applications: OFDM modems, software defined radio, multichannel coding and many other high-speed real-time systems.