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A Radix-4/8/split Radix FFT with Reduced Arithmetic Complexity Algorithm


Affiliations
1 Department of Electrical & Electronics Engineering, Muffakham Jah College of Engineering and Technology, India
2 Department of Electrical Engineering, Indian Institute of Technology Hyderabad, India
3 Department of Electrical and Electronics Engineering, Royal Institute of Technology and Science, India
     

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In this paper we present alternate form of Radix-4/8 and split radix FFT’s based on DIF (decimation in frequency) version and discuss their implementation issues that further reduces the arithmetic complexity of power-of-two discrete Fourier Transform. This is achieved with circular shift operation on a subset of the output samples resulting from the decomposition in these FFT algorithms and a proposed dynamic scaling. These modifications not only provide saving in the calculation of twiddle factor, but also reduce the total flop count to ≈4Nlog2N almost 6% fewer than the standard Radix-4 FFT algorithm ≈ 3×11/12Nlog2N, 5% fewer than the standard Radix-8 FFT, and ≈3×7/9Nlog2N, 5.5% fewer than the standard split radix FFT.

Keywords

DFT (Discrete Fourier Transform), FFT (Fast Fourier Transform), Radix-4(R4), Radix-8(R8) and Split Radix (SR) FFT and Flop Count.
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  • A Radix-4/8/split Radix FFT with Reduced Arithmetic Complexity Algorithm

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Authors

Shaik Qadeer
Department of Electrical & Electronics Engineering, Muffakham Jah College of Engineering and Technology, India
Mohammed Zafar Ali Khan
Department of Electrical Engineering, Indian Institute of Technology Hyderabad, India
Syed Abdul Sattar
Department of Electrical and Electronics Engineering, Royal Institute of Technology and Science, India

Abstract


In this paper we present alternate form of Radix-4/8 and split radix FFT’s based on DIF (decimation in frequency) version and discuss their implementation issues that further reduces the arithmetic complexity of power-of-two discrete Fourier Transform. This is achieved with circular shift operation on a subset of the output samples resulting from the decomposition in these FFT algorithms and a proposed dynamic scaling. These modifications not only provide saving in the calculation of twiddle factor, but also reduce the total flop count to ≈4Nlog2N almost 6% fewer than the standard Radix-4 FFT algorithm ≈ 3×11/12Nlog2N, 5% fewer than the standard Radix-8 FFT, and ≈3×7/9Nlog2N, 5.5% fewer than the standard split radix FFT.

Keywords


DFT (Discrete Fourier Transform), FFT (Fast Fourier Transform), Radix-4(R4), Radix-8(R8) and Split Radix (SR) FFT and Flop Count.