scholarly journals Investigation of the Indirect Hypercube as Natural Architecture for Parallel Algorithms of a Transpose Type for FFT and Other Fourier-Related Transforms

2014 ◽  
Vol 11 (2) ◽  
pp. 29-44
Author(s):  
Ph. Philipov ◽  
V. Lazarov
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Parallel Implementation ◽  
Performance Estimation ◽  
Signal Graph ◽  
Long Time ◽  
Fft Algorithms ◽  
Natural Architecture ◽  
Further Development ◽  
Parallel Fft

Abstract The natural architectures are architectures, derived from the signal graph of the corresponding algorithm. That is why they are considered to be the most appropriate architectures for parallel realization of this algorithm. For Fast Fourier Transform algorithm (FFT) two types of natural architectures are known – the direct and the indirect hypercube. The direct hypercube has been investigated and analyzed a long time ago. The development of the concept of Indirect Hypercube, although quite old, is too difficult, controversal and still unfinished. Fast Hartley transform (FHT)/Real-valued Fast Fourier transform (RFFT) algorithms are important Fourier-related transforms, because they lower twice the operational and memory requirements when the input data is real-valued. These types of algorithms, however, have an irregular computational structure, which makes their parallel implementation a very difficult task. The aim of this paper is, based on the results achieved so far, to present further development of the concept Indirect Hypercube. A method of parametric synthesis of an indirect hypercube is described as a model of parallel FFT algorithms of a transpose type with different granularity/radix. This method is generalized for relevant RFFT/FHT and FCT algorithms. Two types of SIMD array architectures are described (radix-2 and radix-4), based on the indirect hypercube concept. These architectures are implemented as fast FFT/RFFT/FHT processors for real time applications. The performance estimation, as well as the estimation of resource utilization is carried out.

scholarly journals On Performance of Sparse Fast Fourier Transform Algorithms Using the Aliasing Filter

Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1117
Author(s):  
Bin Li ◽  
Zhikang Jiang ◽  
Jie Chen
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
High Efficiency ◽  
Theory And Practice ◽  
Long Time ◽  
And Performance ◽  
Binary Tree Search ◽  
The One ◽  
Sparse Fast Fourier Transform ◽  
L1 And L2

Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete Fourier transform (DFT) by their unique methods so far. In order to use them properly, the urgent topic of great concern is how to analyze and evaluate the performance of these algorithms in theory and practice. This paper mainly discusses the technology and performance of sFFT algorithms using the aliasing filter. In the first part, the paper introduces the three frameworks: the one-shot framework based on the compressed sensing (CS) solver, the peeling framework based on the bipartite graph and the iterative framework based on the binary tree search. Then, we obtain the conclusion of the performance of six corresponding algorithms: the sFFT-DT1.0, sFFT-DT2.0, sFFT-DT3.0, FFAST, R-FFAST, and DSFFT algorithms in theory. In the second part, we make two categories of experiments for computing the signals of different SNRs, different lengths, and different sparsities by a standard testing platform and record the run time, the percentage of the signal sampled, and the L0, L1, and L2 errors both in the exactly sparse case and the general sparse case. The results of these performance analyses are our guide to optimize these algorithms and use them selectively.

IMPLEMENTING FAST FOURIER TRANSFORMS ON DISTRIBUTED-MEMORY MULTIPROCESSSORS USING DATA REDISTRIBUTIONS

1994 ◽  
Vol 04 (04) ◽  
pp. 477-488 ◽  
Author(s):  
S.K.S. GUPTA ◽  
C.-H. HUANG ◽  
P. SADAYAPPAN ◽  
R.W. JOHNSON
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Distributed Memory ◽  
Fourier Transforms ◽  
Experimental Performance ◽  
Minimum Number ◽  
Data Redistribution ◽  
Using Data ◽  
Performance Results ◽  
Fft Algorithms

Implementations of various fast Fourier transform (FFT) algorithms are presented for distributed-memory multiprocessors. These algorithms use data redistribution to localize the computation. The goal is to optimize communication cost by using a minimum number of redistribution steps. Both analytical and experimental performance results on the Intel iPSC/860 system are presented.

The fast Fourier transform

2020 ◽  
pp. 134-189
Author(s):  
Rob H. Bisseling
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Weather Forecasting ◽  
Data Access ◽  
Regular Pattern ◽  
Matrix Products ◽  
Data Redistribution ◽  
Fft Algorithms ◽  
Matrix Vector

This chapter demonstrates the use of different data distributions in different phases of a parallel fast Fourier transform (FFT), which is a regular computation with a predictable but challenging data access pattern. Both the block and cyclic distributions are used and also intermediates between them. Each required data redistribution is a permutation that involves communication. By making careful choices, the number of such redistributions can be kept to a minimum. FFT algorithms can be concisely expressed using matrix/vector notation and Kronecker matrix products. This notation is also used here. The chapter then shows how permutations with a regular pattern can be implemented more efficiently by packing the data. The parallelization techniques discussed for the specific case of the FFT are also applicable to other related computations, for instance in signal processing and weather forecasting.

scholarly journals Empirical Evaluation of Typical Sparse Fast Fourier Transform Algorithms

2020 ◽  
Author(s):  
Bin Li ◽  
Zhikang Jiang ◽  
Jie Chen
Keyword(s):  
Fourier Transform ◽  
Theoretical Analysis ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Empirical Evaluation ◽  
Theoretical Research ◽  
Sparse Signal ◽  
Standard Testing ◽  
Long Time ◽  
Sparse Fast Fourier Transform

Abstract Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal's inherent characteristics that a large number of signals are sparse in the frequency domain. More than ten sFFT lgorithms have been proposed, which can be classfied into many types according to filter, framework, method of location, method of estimation. In this paper, the technology of these algorithms is completely analyzed in theory. The performance of them is thoroughly tested and verified in practice. The theoretical analysis includes the following contents: five operations of ignal, three methods of frequency bucketization, five methods of location, four methods of estimation, two problems caused by bucketization, three methods to solve these two problems, four algorithmic frameworks. All the above technologies and methods are introduced in detail and examples are given to illustrate the above research. After theoretical research, we make experiments for computing the signals of different SNR, N, K by a standard testing platform and record the run time, percentage of the signal sampled and L0;L1;L2 error with eight different sFFT algorithms. The result of experiments satisfies the inferences obtained in theory.

scholarly journals Method for measuring the azimuth of an aerial target for a meter-range radar

2021 ◽  
pp. 26-31
Author(s):  
V. I. Ermoshkin ◽  
S. B. Shatkovsky ◽  
A. V. Shcherbinko ◽  
E. E. Fenyuk
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Antenna Array ◽  
New Method ◽  
Test Results ◽  
Radio Waves ◽  
Statistical Estimates ◽  
Pulse Processing ◽  
The Mean ◽  
Further Development

The purpose of the study is to develop a new method that increases the accuracy of measuring the azimuth of an air target for stationary radars of the meter range of radio waves with a fixed antenna array and a small number of antenna elements. For this, the known methods are considered and their disadvantages are revealed. The new method proposed by the authors uses a digital radiation pattern with a fast Fourier transform after intra-pulse processing of signals from the receiving elements of the antenna array at a given frequency. To refine the azimuth, an inverse fast Fourier transform is used, followed by signal processing and repeated measurement for each target with a small step. Calculations and test results are presented. Comparisons of statistical estimates of the mean and standard deviation of azimuth measurement tests by various methods are presented. The scientific novelty and directions for further development of the topic with the use of the results obtained have been established.

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