A Radix-2 DIT FFT with reduced arithmetic complexity

The efficient computation of Discrete Fourier Transform (DFT) is an important issue as it is used in almost all fields of engineering for signal processing. This paper presents a different form of Radix-2 Fast Fourier Transform (FFT) based on Decimation in time (DIT) to compute DFT, discuss their implementation issues and derive it´s signal to quantization noise ratio(SQNR) that further decreases the number of multiplication counts without affecting the number of additions of Radix-2 discrete Fourier Transform. It is achieved by simple scaling of Twiddle factor (TF) using a special scaling factor. This modification not only decreases the total flop counts from 5Nlog₂N to ≈ 42/3 Nlog₂N (6.66% fewer than the standard Radix-2 FFT algorithm) but also improves SQNR from 1 over 2N2^-2b to 9 over 15N2^-2b (1.6dB more than the standard Radix-2 FFT algorithm).