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

Shaik Qadeer; Mohammed Zafar Ali Khan; Syed Abdul Sattar

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

Shaik Qadeer ¹, Mohammed Zafar Ali Khan ², Syed Abdul Sattar ³

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

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.