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.

An area efficient high speed optimized FFT algorithm

Abstract: In recent years the Fast Fourier Transform is widely used in a number of applications as it is considered to be an efficient algorithm to compute the Discrete Fourier Transform. The process of computing the FFT for large sequence real time data becomes complex and tedious. Hence it is necessary to design a system that can perform the FFT computation of large sequence data with reduced power consumption. This paper presents the design of low power Radix-8 DIT FFT. The proposed design aims at reducing the number of multipliers that are used to compute the FFT. This is achieved by swapping the input terms and reordering them. This leads to a reduction in the number of multipliers used to perform the computation and thereby causing a reduction in the power consumption. This method is highly advantageous when the input signals are lengthy since the number of multipliers used is large in number consuming very high power. In order to optimize the FFT architecture the number of multipliers is reduced thereby causing a significant reduction in power. The prototype for Radix-2 (8 point) and Radix-4 (16 point) optimized FFT is designed, implemented and simulated using Altera ModelSim DE2 EP2C35F672C6 FPGA device. The proposed Radix-2 (8 point) and Radix-4 (16 point) optimized FFT operates at a speed of 10.41 Gbps and 21.23 Gbps respectively.

The fast Fourier transform its role as an algebraic algorithm

Abstract: In the past decade the Cooley-Tukey fast Fourier transform (FFT) [1] has achieved the status of a “super” algorithm. As a numerical (complex field) algorithm, the FFT has revolutionized large scale time series analysis in a way that counts most—economic. (See, e.g., Refs. 3-6.) Since the late sixties, the FFT has also emerged as an important algebraic(abstract field) algorithm, with many interesting applications to the theory and practice of algebraic computing. The abstract character of the FFT, in particular its role as an algebraic algorithm, is what this paper is about.Our discussion centres around the following questions:1. What is the discreteFourier transform?2. What is the fastFourier transform?3. What is its role in algebraiccomputing?4. Is a finite field(mod p) FFT feasible?

A structured review of sparse fast Fourier transform algorithms

Abstract: Discrete Fourier transform (DFT) implementation requires high computational resources and time; a computational complexity of order O(N2) for a signal of size N. Fast Fourier transform (FFT) algorithm, that uses butterfly structures, has a computational complexity of O(Nlog(N)), a value much less than O(N2). However, in recent years by introducing big data in many applications, FFT calculations still impose serious challenges in terms of computational complexity, time requirement, and energy consumption. Involved data in many of these applications are sparse in the spectral domain. For these data by using Sparse Fast Fourier Transform (SFFT) algorithms with a sub-linear computational and sampling complexity, the problem of computational complexity of Fourier transform has been reduced substantially. Different algorithms and hardware implementations have been introduced and developed for SFFT calculations. This paper presents a categorized review of SFFT, highlights the differences of its various algorithms and implementations, and also reviews the current use of SFFT in different applications.

A serial minded FFT

Abstract: An FFT algorithm is presented that can be implemented with serial-access memory. For clarity and insight the emphasis is upon conciseness and illustration rather than shorthand mathematical notation. The algorithm's potential for high-speed implementation is demonstrated by studying variations on the basic algorithm that include both higher radix algorithms and parallel arithmetic unit algorithms. The fact that these sophisticated variations can be seen and understood by inspection of the basic algorithm emphasizes its simplicity. The algorithm is shown very suitable for efficient special-purpose implementation by the functional independence of the transform node from the particular node in the transform or the number of nodes in the transform, i.e., one node in canonical form (for a given radix) represents the entire FFT algorithm. The algorithm is shown to perform variable length transforms at full operational efficiency with minor modification, thus emphasizing its relative versatility. The possibly unexpected conclusion is made that the FFT implementation using parallel arithmetic units is more efficient in terms of speed and probably design effort and hardware, than one using high radix algorithms.

Vector Radix 2 × 2 Sliding Fast Fourier Transform

Abstract: The two-dimensional (2D) discrete Fourier transform (DFT) in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT) algorithm based on the vector radix (VR) 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.