Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.

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.

Algorithm of image information hiding based on new anti-Arnold transform and Blending in DCT domain

Abstract: Traditional Arnold transform is used widely in information hiding technology, but because of its long transform periodicity, it costs large time and computation memory. This paper introduces an new anti-Arnold transform algorithm, which reduces iterative times of anti-transform. With the combination of image blending, discrete cosine transform and new anti-Arnold transform, an algorithm based on the three technologies is proposed. Experimental result shows that the algorithm has good imperceptibility and validity, it also has certain degree of robustness under some common noise and spiteful attack.

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.

Modular pipeline fast fourier transform algorithm

Abstract: A modular pipeline architecture for computing discrete Fourier transforms (DFT) is demonstrated. For an N point DFT, two conventional pipeline N point fast Fourier transform (FFT) modules are joined by a specialized center element. The center element contains memories, multipliers and control logic. Compared with a standard N point pipeline FFT, the modular pipeline FFT reduces the number of delay lines required. Further, the coefficient memory is concentrated within the center element, reducing the storage requirements in each of the conventional FFT modules. The centralized memory and address generator provide the data storage and reordering. The data throughput of a conventional pipeline architecture is maintained with a slightly higher end-to-end latency. The architecture and control logic for both a radix-2 and radix-4 modular pipeline FFT is explained and compared to the traditional pipeline FFT. Further, this methodology facilitates the hardware computation of long FFTs when compared to previous techniques. The new logic developed to control the FFT unit is similar in complexity to current systems and does not rely on any exotic components or hardware features. In fact, the control logic can be reduced to a single counter and a handful of combinational logic. Specifically, using the modular FFT algorithm reduces the overall complexity of the hardware pipeline, permits the use of reusable modules, and does not impact the throughput. The reduction in delay lines lowers the dynamic power consumption. The hardware architecture is particularly suited to reprogrammable and custom devices. Simulations are conducted to analyze the architecture. Experimental results for both radix-2 and radix-4 FFTs are presented and compared with the conventional pipeline FFT. A numerical analysis of the modular pipeline FFT is performed and compared to that of a conventional pipeline FFT.