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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.


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Proceedings ArticleDOI
01 Jan 2004
TL;DR: Both the theory and the simulations show that, pro weighted zoom FFT method has lower computational complexity, less memory need and negligible error, and can meet the need of real-time processing.
Abstract: This paper addresses the problem of fast computation of the ambiguity function using a new method based on pre-weighted zoom FFT algorithm, which employs zoom FFT technique and performs the weighting process previously and thus gets ride of the extra computation. The computational complexity of the presented algorithm is compared with other methods and the simulation results are given. Both the theory and the simulations show that, pro weighted zoom FFT method has lower computational complexity, less memory need and negligible error, and can meet the need of real-time processing.

13 citations

Journal ArticleDOI
TL;DR: A watermarking scheme based on finite radon transform (FRAT), fractional Fourier Transform (FRFT) and singular value decomposition is proposed, which provides additional degree of freedom in security, robustness, payload capacity and visual transparence.
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.

13 citations

Journal ArticleDOI
TL;DR: This paper presents a fast split-radix- (2×2)/(8-times;8) algorithm for computing the 2-D discrete Hartley transform (DHT) of length N ×N with N = q · 2 m, where q is an odd integer.
Abstract: This paper presents a fast split-radix- (2t2)/(8t8) algorithm for computing the 2-D discrete Hartley transform (DHT) of length N ×N with N = q · 2 m, where q is an odd integer. The proposed algorithm decomposes an N × N DHT into one N /2 × N /2 DHT and 48 N /8 × N /8 DHTs. It achieves an efficient reduction on the number of arithmetic operations, data transfers and twiddle factors compared to the split-radix-(2×2)/(4×4) algorithm. Moreover, the characteristic of expression in simple matrices leads to an easy implementation of the algorithm. If implementing the above two algorithms with fully parallel structure in hardware, it seems that the proposed algorithm can decrease the area complexity compared to the split-radix-(2×2)/(4×4) algorithm, but requires a little more time complexity. An application of the proposed algorithm to 2-D medical image compression is also provided.

13 citations

Proceedings ArticleDOI
20 Mar 2016
TL;DR: This paper proposes to leverage the recently introduced Flexible Approximate MUltilayer Sparse Transforms (FAST) in order to compute approximate FFTs on graphs, showing good potential.
Abstract: Signal processing on graphs is a recent research domain that seeks to extend classical signal processing tools such as the Fourier transform to irregular domains given by a graph. In such a graph setting, a way to rapidly apply the Fourier transform, i.e. a Fast Fourier Transform (FFT), is lacking. In this paper, we propose to leverage the recently introduced Flexible Approximate MUlti-layer Sparse Transforms (FAST) in order to compute approximate FFTs on graphs. The approach is first described, then validated on several types of classical graphs and finally used for fast filtering, showing good potential.

13 citations

01 Nov 1987
TL;DR: This thesis investigates several different aspects of parallel Fast Fourier Transform implementation techniques for distributed-memory message-passing systems such as hypercube multiprocessors with excellent speedup when implemented on the Intel iPSC hypercube.
Abstract: The Fast Fourier Transform appears frequently in scientific computing. Therefore it is desirable to implement it efficiently on parallel computers. In this thesis, we investigate several different aspects of parallel Fast Fourier Transform implementation techniques for distributed-memory message-passing systems such as hypercube multiprocessors. We describe various Fast Fourier Transform algorithms using a matrix notation. An error analysis is presented that considers the effect of different methods used in the computation of the Fourier Transform coefficients as well as accumulated roundoff. New implementations of one and two-dimensional Fast Fourier Transforms are presented along with comparisons with existing methods. New algorithms for symmetric transforms are also developed and the results show excellent speedup when implemented on the Intel iPSC hypercube.

13 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
202224
20211
20188
201757
201692