Showing papers on "Prime-factor FFT algorithm published in 2017"

Correcting soft errors online in fast fourier transform

Abstract: While many algorithm-based fault tolerance (ABFT) schemes have been proposed to detect soft errors offline in the fast Fourier transform (FFT) after computation finishes, none of the existing ABFT schemes detect soft errors online before the computation finishes. This paper presents an online ABFT scheme for FFT so that soft errors can be detected online and the corrupted computation can be terminated in a much more timely manner. We also extend our scheme to tolerate both arithmetic errors and memory errors, develop strategies to reduce its fault tolerance overhead and improve its numerical stability and fault coverage, and finally incorporate it into the widely used FFTW library - one of the today's fastest FFT software implementations. Experimental results demonstrate that: (1) the proposed online ABFT scheme introduces much lower overhead than the existing offline ABFT schemes; (2) it detects errors in a much more timely manner; and (3) it also has higher numerical stability and better fault coverage.

A Memory-Based FFT Processor Design With Generalized Efficient Conflict-Free Address Schemes

Abstract: This paper presents the design and implementation of memory-based fast Fourier transform (FFT) processors with generalized efficient, conflict-free address schemes. We unified the conflict-free address schemes of three different FFT lengths, including the single-power points, the common nonsingle-power points, and the nonsingle-power points applied with a prime factor algorithm. Though the three cases differ in terms of decomposition, they are all compatible with memory-based architecture by the way of the proposed address schemes. Moreover, the decomposition algorithm utilizes a method, named high-radix–small-butterfly (HRSB), to decrease the computation cycles and eliminate the complexity of the processing engine. In addition, an efficient index generator, a simplified multipath delay commutator engine, and a unified Winograd Fourier transform algorithm butterfly core were also designed. We designed two FFT examples in long-term evolution system to verify the availability of the address scheme, including a 2n (128–2048)-point FFT unit and a 35 different point (12–1296) DFT unit. Compared with previous works with similar address schemes, this paper supports more generalized lengths and achieves more flexible throughput.

Hybrid Genetic Algorithm and Modified Iterative Fourier Transform Algorithm for Large Thinned Array Synthesis

Abstract: In this letter, a hybrid algorithm based on the genetic algorithm (GA) and modified iterative Fourier transform (MIFT) technique called HGAMIFT is proposed for large thinned array synthesis. By employing a perturbation mechanism, the MIFT can achieve a better solution in terms of the peak sidelobe level when compared to the iterative Fourier transform technique. Moreover, a control factor to determine the proportion of individuals from GA and MIFT as well as the crossover and mutation rate is introduced to help the HGAMIFT maintain the diversity of population in the early phase while avoiding stagnation in the late phase. Thus, a resulting enhanced search ability and fast convergence velocity can be obtained simultaneously. Several thinned arrays that comprise different array sizes and aperture shapes have been synthesized, which validate the superior performance of the proposed algorithm.

Improvement in Computation Time of 3-D Scattering Center Extraction Using the Shooting and Bouncing Ray Technique

Abstract: We present a fast 3-D scattering center extraction algorithm using the shooting and bouncing ray technique. The proposed algorithm generates a 3-D inverse synthetic aperture radar image from which a set of 3-D scattering centers is then extracted using the CLEAN algorithm. In the conventional extraction algorithm, computation time is improved using the fast Fourier transform (FFT)-based scheme. However, the memory requirement is greatly increased because of the high oversampling required to mitigate the interpolation error. Evaluation of memory-time tradeoffs indicates that the conventional algorithm is still too time consuming given the constraints of practical memory. Thus, a modified FFT-based scheme is proposed to improve computation time without increasing the memory requirement. Through modifying the ray spread function, the distortion from the interpolation error is mitigated without the use of high oversampling. Implementation based on the proposed FFT-based scheme accelerates the image formation process significantly. Numerical simulations of realistic targets are presented to demonstrate the performance of the proposed algorithm.

Guaranteed-Stable Sliding DFT Algorithm With Minimal Computational Requirements

Abstract: The discrete Fourier transform (DFT) is the most widely used technique for determining the frequency spectra of digital signals. However, in the sliding transform scenario where the transform window is shifted one sample at a time and the transform process is repeated, the use of DFT becomes difficult due to its heavy computational burden. This paper proposes an optimal sliding DFT (oSDFT) algorithm that achieves both the lowest computational requirement and the highest computational accuracy among existing sliding DFT algorithms. The proposed oSDFT algorithm directly computes the DFT bins of the shifted window by simply adding (or subtracting) the bins of a previous window and an updating vector. We show that the updating vector can be efficiently computed with a low complexity in the sliding transform scenario. Our simulations demonstrate that the proposed algorithm outperforms the existing sliding DFT algorithms in terms of computational accuracy and processing time.

FFT and sparse FFT techniques and applications

Abstract: Currently, the FFT is used in different areas, starting from identification of frequency on mechanical vibration to image enhancement. Real-time computation by interpret the acquired data can be easily possible by Fast Fourier Transform (FFT). The best with an efficient algorithm is FFT so it is the foundation for analyzing, monitoring, and controlling various systems. Many applications like digital signal processing, partial differential equation solvers, communications, image processing, all most all Fourier coefficients are very small and known as sparse. In this paper we present different impact of fft and sparse fft in the areas of medical imaging, wireless communication.

Elementary Number Theory and Rader's FFT

Abstract: This note provides a self-contained introduction to Rader's fast Fourier transform (FFT). We start by explaining the need for an additional type of FFT. The properties of the multiplicative group o...

Area-Time Efficient Architecture of FFT-Based Montgomery Multiplication

Abstract: The modular multiplication operation is the most time-consuming operation for number-theoretic cryptographic algorithms involving large integers, such as RSA and Diffie-Hellman. Implementations reveal that more than 75 percent of the time is spent in the modular multiplication function within the RSA for more than 1,024-bit moduli. There are fast multiplier architectures to minimize the delay and increase the throughput using parallelism and pipelining. However such designs are large in terms of area and low in efficiency. In this paper, we integrate the fast Fourier transform (FFT) method into the McLaughlin’s framework, and present an improved FFT-based Montgomery modular multiplication (MMM) algorithm achieving high area-time efficiency. Compared to the previous FFT-based designs, we inhibit the zero-padding operation by computing the modular multiplication steps directly using cyclic and nega-cyclic convolutions. Thus, we reduce the convolution length by half. Furthermore, supported by the number-theoretic weighted transform, the FFT algorithm is used to provide fast convolution computation. We also introduce a general method for efficient parameter selection for the proposed algorithm. Architectures with single and double butterfly structures are designed obtaining low area-latency solutions, which we implemented on Xilinx Virtex-6 FPGAs. The results show that our work offers a better area-latency efficiency compared to the state-of-the-art FFT-based MMM architectures from and above 1,024-bit operand sizes. We have obtained area-latency efficiency improvements up to 50.9 percent for 1,024-bit, 41.9 percent for 2,048-bit, 37.8 percent for 4,096-bit and 103.2 percent for 7,680-bit operands. Furthermore, the operating latency is also outperformed with high clock frequency for length-64 transform and above.

A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform

Abstract: In this work, a fast and accurate chirp-rate estimation algorithm is presented. The algorithm is based on the fractional Fourier transform. It is shown that utilization of the golden section search algorithm to find the maximum magnitude of the fractional Fourier transform domains not only accelerates the process, but also increases the accuracy in a noisy environment. Simulation results validate the proposed algorithm and show that the accuracy of parameter estimation nearly achieves the Cramer-Rao lower bound for SNR values as low as −7dB.

Hybrid Watermarking Algorithm using Finite Radon and Fractional Fourier Transform

Abstract: Watermarking is proposed as solution to authentication, copyright protection and security requirements of multimedia objects (speech, image and video). In this paper a watermarking scheme based on finite radon transform (FRAT), fractional Fourier Transform (FRFT) and singular value decomposition is proposed. In the proposed scheme, image to be watermarked is first transformed by finite radon transform, the radon transformed image is further transformed by FRFT, and singular values of FRFT transformed image are modified to embed the watermark. Inverse transformation is applied to obtain watermarked image. Simulations are performed under various test conditions with different FRFT transform angles for improved robustness and visual transparence of watermarked image. Results of the proposed scheme are better in comparison to the existing schemes for most of the attacks. Proposed scheme provide additional degree of freedom in security, robustness, payload capacity and visual transparence. Proposed scheme can also be used to communicate or store the watermarked image as erasure code, to reduce communication errors over a network, due to the use of FRAT.

Coded Fourier Transform

Abstract: We consider the problem of computing the Fourier transform of high-dimensional vectors, distributedly over a cluster of machines consisting of a master node and multiple worker nodes, where the worker nodes can only store and process a fraction of the inputs. We show that by exploiting the algebraic structure of the Fourier transform operation and leveraging concepts from coding theory, one can efficiently deal with the straggler effects. In particular, we propose a computation strategy, named as coded FFT, which achieves the optimal recovery threshold, defined as the minimum number of workers that the master node needs to wait for in order to compute the output. This is the first code that achieves the optimum robustness in terms of tolerating stragglers or failures for computing Fourier transforms. Furthermore, the reconstruction process for coded FFT can be mapped to MDS decoding, which can be solved efficiently. Moreover, we extend coded FFT to settings including computing general $n$-dimensional Fourier transforms, and provide the optimal computing strategy for those settings.

A Continuous-Flow Memory-Based Architecture for Real-Valued FFT

Abstract: This brief proposes a continuous-flow memory-based architecture for fast Fourier transform (FFT) computation for real-valued signals. The proposed architecture is based on a modified radix-2 algorithm, which removes redundant operations to reduce resource usage. A new data-flow graph and address mapping scheme are proposed that satisfy the requirement of continuous-flow operation and minimize the memory usage. The proposed processing element takes advantage of pipelined FFT architectures to avoid bank conflicts in each stage. Compared with prior works, the proposed design has the advantage of supporting continuous-flow operation and normal-order output while minimizing the resource usage.

The Sliding Windowed Infinite Fourier Transform [Tips & Tricks]

Abstract: The discrete Fourier transform (DFT) is the standard tool for spectral analysis in digital signal processing, typically computed using the fast Fourier transform (FFT). However, for real-time applications that require recalculating the DFT at each sample or over only a subset of the N center frequencies of the DFT, the FFT is far from optimal.

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.

Optimized Spectrum Permutation for the Multidimensional Sparse FFT

Abstract: A multidimensional sparse fast Fourier transform algorithm is introduced via generalizations of key concepts used in the one-dimensional (1-D) sparse Fourier transform algorithm. It is shown that permutation parameters are of key importance and should not be chosen randomly but instead can be optimized. A connection is made between the sparse Fourier transform algorithm and lattice theory, thus establishing a rigorous understanding of the effect of the permutations on the algorithm performance. Lattice theory is then used to optimize the set of parameters to achieve a more robust and better performing algorithm. Other algorithms using pseudorandom spectrum permutation can also benefit from the methods developed in this paper. The contributions address the case of the exact $k$ -sparse Fourier transform but the underlying concepts can be applied to the general case of finding a $k$ -sparse approximation of the Fourier transform of an arbitrary signal. Simulations illustrate the efficiency and accuracy of the proposed algorithm. The optimizations of the parameters and the improved performance are shown in simulations for the 2-D case where worst case and average case peak signal-to-noise ratio (PSNR) improves by several decibels.

Fast interpolation of bandlimited functions

Abstract: The nonuniform fast Fourier transform comprises a set of algorithms which approximately interpolate the usual discrete Fourier transform in the time and/or frequency domain. A nonuniform fast Fourier transform based on the fast multipole method was previously developed but passed over in favor of other approaches [1, 2]. This work extends a recent method for computing a periodized fast multipole method [3] with an adaptive algorithm that reduces the required number of multipole-to-local and local-to-local translations by an order of magnitude. This combination improves the speed and accuracy of the original algorithm, and results in an algorithm that is competitive with other nonuniform fast Fourier transforms. Numerical experiments are carried out comparing our implementation with others, demonstrating its viability.

The Truncated Fourier Transform for Mixed Radices

Abstract: The standard version of the Fast Fourier Transform (FFT) is applied to problems of size n=2k. For this reason, FFT-based evaluation interpolation schemes often reduce a problem of size l to a problem of size n , where n is the smallest power of two with l ≤ n. However, this method presents "jumps" in the complexity at powers of two; and on the other hand, n-l values are computed that are actually unnecessary for the interpolation. To mitigate this problem, a truncated variant of the FFT was designed to avoid the computation of these unnecessary values. In the initial formulation [10], it is assumed that n is a power of two, but some use cases (for example in finite fields) may require more general values of n. This paper presents a generalization of the Truncated Fourier Transform (TFT) for arbitrary orders. This allows to benefit from the advantages of the TFT in the general case.

Fast Fourier transform benchmark on X86 Xeon system for multimedia data processing

Abstract: I benchmarking the well-known Fast Fourier Transforms Library at X86 Xeon E5 2690 v3 system. Fourier transform image processing is an important tool that is used to decompose the image into sine and cosine components. If the input image represented by the equation in the spatial domain, output from the Fourier transform represents the image in the fourier or the frequency domain. Each point represents a particular frequency included in the spatial domain image in the Fourier domain image. Fourier transform is used widely for image analysis, image filtering, image compression and image reconstruction as a wide variety of applications. Fourier transform plays a important role in signal processing, image processing and speech recognition. It has been used in a wide range of sectors. For example, this is often a signal processing, is used in digital signal processing applications, such as voice recognition, image processing. The Discrete Fourier transform is a specific kind of Fourier transform. It maps the sequence over time to sequence over frequencies. If it implemented as a discrete Fourier transform, the time complexity is O (N2). It's actually not a better way to use. Alternatively, the Fast Fourier Transform is possible to easily perform a Discrete Fourier Transform of parallelism with only O (n log n) algorithm. Fast Fourier Transform is widely used in a variety of scientific computing program. If you are using the correct library can improve the performance of the program, without any additional effort. I have a well-known fast Fourier transform library was going to perform a benchmarking on X86 based Intel Xeon E5 2690 systems. In the machine's current Intel Xeon X86 Linux system. I have installed Intel IPP library, FFTW3 Library (West FFT), Kiss -FFT library and the numutils library on Intel X86 Xeon E5 based systems. The benchmark performed at C, and measuring the performance over a range of a transform size. It benchmarks both real and complex transforms in one dimension.

Sparse fast Clifford Fourier transform

Abstract: The Clifford Fourier transform (CFT) can be applied to both vector and scalar fields However, due to problems with big data, CFT is not efficient, because the algorithm is calculated in each semaphore The sparse fast Fourier transform (sFFT) theory deals with the big data problem by using input data selectively This has inspired us to create a new algorithm called sparse fast CFT (SFCFT), which can greatly improve the computing performance in scalar and vector fields The experiments are implemented using the scalar field and grayscale and color images, and the results are compared with those using FFT, CFT, and sFFT The results demonstrate that SFCFT can effectively improve the performance of multivector signal processing

FFT-Based Method With Near-Matrix Compression

Abstract: In this paper, a novel grouping scheme of the basis functions within the framework of the fast Fourier transform (FFT)-based method is proposed for creating a block-sparse structure for the near-matrix, and then FFT-based method with near-matrix compression is established for the efficient analysis of multiscale problems. For a multiscale problem, if an FFT-based method is required to maintain both higher efficiency and higher accuracy at calculating the far interactions, then the near-matrix will be inevitably very large. Compared with the traditional FFT-based method, the proposed method can significantly reduce the near-matrix memory requirement without increasing the time spent. Several numerical examples are provided to demonstrate the correctness and the efficiency of the proposed method.

Parallel Nonuniform Discrete Fourier Transform (P-NDFT) Over a 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 (WSNs) Meanwhile, Fourier transforms are among the most widely used frequency analysis tools in WSNs for studying the behavior of sensed phenomena Several energy-efficient in-network Fourier transform computation algorithms have been proposed for WSNs Most of these works assume that the sensors are equally spaced over a one-dimensional (1D) region However, in practice, the sensors are usually randomly distributed over a two-dimensional (2D) plane Consequently, the conventional 2D Fast Fourier Transform (FFT) designed for data sampled on a uniform grid is not applicable in such environments We address this problem by designing a distributed hybrid structure consisting of local Non-equispaced Discrete Fourier Transform (NDFT) and global FFT computations First, the NDFT method is applied within suitably selected clusters to obtain the initial uniform Fourier coefficients within allowable estimation error bounds We investigate both classical linear and generalized interpolation methods for computing the NDFT coefficients within each cluster Second, a separable 2D FFT is applied over all clusters using our proposed energy-efficient 1D FFT computation method, which reduces communication costs by employing a novel binary representation mapping strategy for data exchanges between sensors The proposed techniques are implemented on the SIDnet-SWANS platform, and the tradeoffs between communication cost, execution time, and energy consumption are studied

Effectiveness of partitioning strategies of Fast Fourier Transform in GPU implementations

Abstract: In this paper authors present the results of the effectiveness comparison between the variants of the Radix-2 Deci-mation in Time (DIT) Fast Fourier Transform (FFT) algorithm's implementations on graphics processing units (GPUs) which differ in the way the calculations are distributed among GPUs computational resources. The conducted experiments show that the partitioning of the FFT computational scheme into 4-point and 8-point subtransform blocks in which calculations are performed in a sequential, single instruction multiple thread (SIMT) manner results in significantly faster execution of the FFT calculations on the selected GPU architectures than the standard parallel 2-point butterfly base operation approach. Moreover the proposed partitioning scheme can be extended to arbitrary subtransform block size for a given N-point Radix-2 FFT implementation dedicated to particular GPU architectures.

An efficient pipelined architecture for real-valued Fast Fourier Transform

Abstract: Real-valued Fast Fourier Transform (FFT) plays an important role in today’s digital world because of the fact that most of the signals contain real values. The FFT computation of real signals using conventional techniques requires more hardware space with high power consumption, which is the most important task for a researcher while designing VLSI architectures. This can be eradicated by clearly analysing the symmetric property of the real-valued signals. In this paper, we have adopted the symmetric property and designed an efficient pipelined architecture for 16-point DIF FFT. The pipeline scheme reduce the processing time at the cost of some registers and in order to contribute efficiently for power reduction we have modified the complex multiplier with reduced internal real multipliers which are in turn replaced by an modified canonic signed digit multiplier (CSDM) with resource-sharing technique. The complete module is synthesised and simulated using Xilinx ISE 14.1 with the target device is ...

Design of a recursive single-bin DFT algorithm for sparse spectrum analysis

Abstract: Discrete Fourier transform (DFT) is the basic means of spectrum analysis in the field of digital signal processing, and the fast Fourier transform (FFT) has become the most popular algorithm which decreases the computational complexity from quadratical to linearithmic. However, engineers are often challenged to detect a single or just a few of the frequency components. For this kind of sparse spectrum analysis, the FFT no longer has advantage because it always computes all the frequency components. This paper proposes a recursive single-bin DFT (RSB-DFT) algorithm to compute one specific frequency spectrum, whose theoretical derivation is elaborated and implementation steps are given as a flow diagram. A 16-point RSB-DFT calculation example is also given to exhibit computation process of the algorithm. An application example for bioimpedance spectroscopy (BIS) measurement demonstrates that the proposed RSB-DFT algorithm can compute specific single spectral lines accurately. The computation efficiency of the proposed RSB-DFT algorithm is demonstrated as the highest compared with the DFT, FFT, Goertzel algorithm, which means that the RSB-DFT algorithm has the potential to become an alternative and efficient tool for sparse spectrum analysis.

High-throughput Low-complexity Mixed-radix FFT Processor using a Dual-path Shared Complex Constant Multiplier

Abstract: This paper presents a high-throughput lowcomplexity 512-point eight-parallel mixed-radix multipath delay feedback (MDF) fast Fourier transform (FFT) processor architecture for orthogonal frequency division multiplexing (OFDM) applications. To decrease the number of twiddle factor (TF) multiplications, a mixed-radix 2 4 /2 3 FFT algorithm is adopted. Moreover, a dual-path shared canonical signed digit (CSD) complex constant multiplier using a multi-layer scheme is proposed for reducing the hardware complexity of the TF multiplication. The proposed FFT processor is implemented using TSMC 90-nm CMOS technology. The synthesis results demonstrate that the proposed FFT processor can lead to a 16% reduction in hardware complexity and higher throughput compared to conventional architectures.

Low-complexity twiddle factor generator for FFT processors

Abstract: This paper presents a low-complexity twiddle factor (TF) generator suitable for radix-8/4/2 fast Fourier transformation (FFT). The proposed TF generator employs a full complex multiplier only and simple logic units to produce all the twiddle factors required for use in FFT computation. This generator approximately costs constant chip area for an arbitrary point of FFT processor, almost independent of the FFT processing size.