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.

Fourier transform algorithm implementations on a general-purpose microprocessor

Abstract: The Fourier representation of sequences plays a key roll in the analysis, the design, and the implementation of digital signal processing algorithms. The existence of very efficient algorithms for computing the Fourier transforms have expanded the importance of Fourier analysis in digital signal processing. To indicate the importance of efficient computational schemes, evaluation of two well-known algorithms - the Cooley-Tukey fast Fourier transform and complex general-N Winograd Fourier transform - were implemented on a general-purpose, high-speed, digital microprocessor - the MC68000. The Despain very fast Fourier algorithm was studied as well. Complexity measures for Fourier transforms, or the relative executional time of an implemented algorithm, have generally been based on the number of multiplications and additions required. For this reason, algorithmic improvements have primarily consisted of reduction in the number of multiplications and additions. However, large amounts of accessing and storing of data, as well as loop control overhead, are inherent in the implementation of these algorithms. Comparisons of the three algorithms as well as numerical versus data transfer operations are presented for a specific microprocessor implementation.

VLSI implementation of an improved multiplier for FFT computation in biomedical applications

Abstract: Discrete Fourier Transform (DFT) is a fundamental Digital Signal Processing domain transformation technique used in many applications for frequency analysis and frequency domain processing. Fast Fourier Transform (FFT) is used for signal processing applications. It consists of addition and multiplication operations, whose speed improvement will enhance the accuracy and performance of FFT computation for any application. It is an algorithm to compute Discrete Fourier Transform (DFT) and its inverse. DFT is obtained by decomposing a sequence of values into components of different frequencies. FFT can compute DFT in O(N log N) operations unlike DFT computation that takes O(N2) arithmetic operations. This reduces computation time by several orders of magnitude and the improvement is roughly proportional to N / log N. Present day Research focus is on performance improvement in computation of FFT specific to field of application. Many performance improvement studies are in progress to implement efficient FFT computation through better performing multipliers and adders. Electroencephalographic (EEG) signals are invariably used for clinical diagnosis and conventional cognitive neuroscience. This work intends to contribute to a faster method of computation of FFT for analysis of EEG signals to classify Autistic data.

Power-Efficient Algorithms for Fourier Analysis over Random Wireless Sensor Network

Abstract: Reduced execution time and increased power efficiency are important objectives in the distributed execution of collaborative signal processing tasks over wireless sensor networks. The power-efficient implementation of the Fourier transform computation is an exemplar of distributed data communication and processing task widely used in the signal processing field. Past work has presented some energy-efficient in-network Fourier transform computation algorithms devised only for uniformly sampled one-dimensional (1D) sensor data. However the circumstance that sensors are randomly distributed over a 2D plane may be more practical, therefore the conventional two-dimensional Fast Fourier Transform (2D FFT) defined for data sampled on uniform grids is not directly applicable in such environments. We address this problem by designing a distributed hybrid structure consisting of local None quispaced Discrete Fourier Transform (NDFT) and global FFT computation. Firstly, NDFT method is applied in a suitable choice of clusters to get the initial uniform Fourier coefficients with allowable estimation error bounds. We experiment with classical linear as well as generalized interpolation methods to compute NDFT coefficients within each cluster. A separable 2D FFT is then performed over all these clusters by employing our proposed energy-efficient 1D FFT computation that reduces communication costs using a novel bit index mapping strategy for data exchanges between sensors. The proposed techniques are implemented in a SID net-SWANS platform to investigate the communication costs, execution time, and energy consumption. Our results show reduced execution time and improved energy consumption when compared with existing work.

An algorithm for a fast two-dimensional discrete cosine transform

Abstract: The authors present an algorithm for the implementation of the two-dimensional discrete cosine transform (DCT) for 2/sup n/*2/sup n/ data points. This algorithm is based on a recently published fast one-dimensional DCT algorithm. The new algorithm is recursive, fast, and numerically stable. The two-dimensional decomposition in this new algorithm is based on the vector-radix approach. In this approach, the data matrix is partitioned into four subblocks, each of which, after some processing is transformed by a lower order DCT. The results from the lower order transforms are then combined to form the desired two-dimensional DCT. The overall complexity of the new transform is compared in terms of the number of multiplications and additions required to perform the two-dimensional DCT with those of a row/column implementation using the fast one-dimensional transform. >