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# ECE 734: Project Presentation PowerPoint PPT Presentation

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),

ECE 734: Project Presentation

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### ECE 734: Project Presentation

64-point FFT Algorithmfor 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),

• 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

• 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

### 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 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 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

• 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: 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.