Split-radix FFT algorithm

About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.

A new memory-based FFT processor for VDSL transceivers

Abstract: This paper presents a new VLSI architecture for fast computation of the N-point discrete Fourier transform (DFT) based on a radix-2 fast algorithm, where N is a power of two. The architecture consists of one complex multiplier, two complex adders, five two-port RAM's, one ROM, and some simple logic circuits. It can evaluate, in average, one DFT sample every (log/sub 2/N)/2 clock cycles. Under 0.35 /spl mu/m CMOS technology, the proposed design is able to operate at a 100 MHz clock rate to compute 22.2M transform samples per second for the case of N=512. The low-complexity and high-throughput feature makes the proposed design attractive for use in high-speed real-time DFT applications, such as the discrete multitone based very-high-rate digital subscriber line transceivers.

An in-place truncated fourier transform and applications to polynomial multiplication

Abstract: The truncated Fourier transform (TFT) was introduced by van der Hoeven in 2004 as a means of smoothing the "jumps" in running time of the ordinary FFT algorithm that occur at power-of-two input sizes. However, the TFT still introduces these jumps in memory usage. We describe in-place variants of the forward and inverse TFT algorithms, achieving time complexity O(n log n) with only O(1) auxiliary space. As an application, we extend the second author's results on space-restricted FFT-based polynomial multiplication to polynomials of arbitrary degree.

A segmented FFT algorithm for vector computers

Abstract: The Fast Fourier Transform algorithm does not readily lend itself to efficient implementation on vector computers, especially on machines where sequential access is important. Several authors have commented that the efficiency of computation is much improved if many transforms are performed simultaneously. We present a new algorithm designed for large, single transforms, which employs a pair of multiple transforms to perform the single transform. The merits of the algorithm are discussed with reference to its implementation on a CDC CYBER 205.

Sparse Fast Fourier Transform by downsampling

Abstract: Sparse Fast Fourier Transform (sFFT) [1][2], has been recently proposed to outperform FFT in reducing computational complexity. Assume that an input signal of length N in the frequency domain is K-sparse, where K ≤ N. sFFT costs O(K logN) instead of O(N logN) in FFT. In this paper, a new fast sFFT algorithm is proposed and costs O(K logK) averagely without any operations being related to N. The idea is to downsample the original input signal at the beginning. Subsequent processing operates under downsampled signals, which length is proportional to O(K). However, downsampling possibly leads to “aliasing.” By shift theorem of DFT, the aliasing problem can be formulated as the “Moment-preserving problem.” In addition, a top-down iterative strategy combined with different downsampling factors further saves computational costs. Complexity analysis and experimental results show that our method outperforms FFT and sFFT.

An efficient multiplierless approximation of the fast Fourier transform using sum-of-powers-of-two (SOPOT) coefficients

Abstract: This letter proposes a new multiplierless approximation of the discrete Fourier transform (DFT) called the multiplierless fast Fourier transform-like (ML-FFT) transformation. It makes use of a novel factorization to parameterize the twiddle factors in the conventional radix-2/sup n/ or split-radix FFT algorithms as certain rotation-like matrices and approximates the associated parameters using the sum-of-powers-of-two (SOPOT) or canonical signed digits (CSD) representations. The ML-FFT converges to the DFT when the number of SOPOT terms used increases and has an arithmetic complexity of O(N log/sub 2/ N) additions, where N = 2/sup m/ is the transform length. Design results show that the NM-FFT offers flexible tradeoff between arithmetic complexity and numerical accuracy in approximating the DFT.