A 2048-point Split-Radix Fast Fourier Transform Computed using Radix-4 Butterfly Units

Abstract

For the low-power consumption of fast fourier transform, Split-radix fast Fourier transforms are widely used. SRFFT uses less number of mathematical calculations amongst the different FFT algorithms. Split-radix FFT has the same signal flow graph that of conventional radix-2/4 FFT’s. Therefore, the address generation method is same for SRFFT as of radix-2. A low power SRFFT architecture with modified butterfly units is presented over here. Here, it is shown that the, a 2048-point SRFFT is computed using radix-4 butterfly unist. Dynamic power is saved, on compromising the use of extra hardware. Here, the architecture size is increased from radix-2 to 4 and the dynamic power consumption is evaluated.

Low‐power fast Fourier transform hardware architecture combining a split‐radix butterfly and efficient adder compressors

“…It occurs because our split‐radix butterfly uses efficient 5‐2 ACs. Some other works have presented power results for the entire FFT with split‐radix butterfly, but some are FPGA‐based reports, such as in [27‐29]. The work in [6] presents a reduced power value, but it only shows full results for the entire FFT in FPGA.…”

“…The primary goal of the different solutions is to reduce the critical path and, consequently, improve the entire FFT architecture's performance, as seen in [14], whose split-radix structure uses the radix-4 butterfly, but in which no power results are presented. The work in [27] also proposes a split-radix FFT based on the radix-4 butterfly. However, the results are only FPGA based and with no evidence of its efficiency since it was only compared against a 1024-point radix-FFT algorithm using new distributed arithmetic.…”

Design and Simulation of a Low-Power and High-Speed Fast Fourier Transform for Medical Image Compression

“…FFT, is used as an improved version of the traditional discrete signal processing tool (discrete Fourier transform), for medical image compression with various drop ratios. FFT is widely used in medical imaging, engineering, communication, and other fields because it transitions quickly from the T-domain to the F-domain and vice versa [1][2][3][4][5][6].…”

“…The speed difference may be huge, especially in long data sets where N may be higher. FFT can compute the DFT for N 2 log r N multiplications and Nlog r N additions corresponding operation alone using twiddle factor W N = e −j2π/N [4,6] since it is using a butterfly operation and computes p ± αq (results six real adds and four real multiplications). As FFTs are staged algorithms, there are log N 2 stages, and each stage has N/2 butterflies, so there should be four.…”

“…For computing sequences, the radix-4 algorithm is comparable to the radix-2 technique in terms of type and speed management. It takes place as follows: the given sequence divides into four parts based on 'n': The given sequence layout in radix- After the division of N-point DFT, it can be computed as the sum of the outputs of four N/4-point DFTs, and these sub-sequences are interconnected with so-called twiddle factors W lk N = e −(j2lπk/N) , l = 0, 1, 2, 3, as shown in (4).…”