Generation of all radix-2 fast Fourier transform algorithms using binary trees

Qureshi, Fahad; Gustafsson, Oscar

doi:10.1109/ecctd.2011.6043634

Cited by 22 publications

(19 citation statements)

References 8 publications

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“…The number of angles in the set, L, is usually a power of two and its value depends on the FFT stage, as well as on the radix and decomposition [1], [4], [38]. Apart from W 4 , which only involves trivial rotations [1] and is very simple to implement, W 8 , W 16 [1], [38].…”

Section: Mcr With Uniform Scalingmentioning

confidence: 99%

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Low-Complexity Multiplierless Constant Rotators Based on Combined Coefficient Selection and Shift-and-Add Implementation (CCSSI)

Garrido

Qureshi

Gustafsson

2014

IEEE Trans. Circuits Syst. I

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Abstract-This paper presents a new approach to design multiplierless constant rotators. The approach is based on a combined coefficient selection and shift-and-add implementation (CCSSI) for the design of the rotators. First, complete freedom is given to the selection of the coefficients, i.e., no constraints to the coefficients are set in advance and all the alternatives are taken into account. Second, the shift-and-add implementation uses advanced single constant multiplication (SCM) and multiple constant multiplication (MCM) techniques that lead to lowcomplexity multiplierless implementations. Third, the design of the rotators is done by a joint optimization of the coefficient selection and shift-and-add implementation. As a result, the CCSSI provides an extended design space that offers a larger number of alternatives with respect to previous works. Furthermore, the design space is explored in a simple and efficient way.The proposed approach has wide applications in numerous hardware scenarios. This includes rotations by single or multiple angles, rotators in single or multiple branches, and different scaling of the outputs.Experimental results for various scenarios are provided. In all of them, the proposed approach achieves significant improvements with respect to state of the art.

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Section: Mcr With Uniform Scalingmentioning

confidence: 99%

“…Apart from W 4 , which only involves trivial rotations [1] and is very simple to implement, W 8 , W 16 [1], [38].…”

Section: Mcr With Uniform Scalingmentioning

confidence: 99%

Low-Complexity Multiplierless Constant Rotators Based on Combined Coefficient Selection and Shift-and-Add Implementation (CCSSI)

Garrido

Qureshi

Gustafsson

2014

IEEE Trans. Circuits Syst. I

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“…10 Fast implementation of DFT algorithm on architecture with constant degree processors is also an area of recent research interest. A number of parallel algorithms developed for DFT/FFT in different architectures can be found in the literature [5]- [9], [11], [14], [30]- [32], [34], [35], [36]- [38]. Parallel implementation of Fourier transform has been discussed and implemented in mesh [30]- [32], binary tree [19] and star graph [34].…”

Section: Comparative Study Of Time Complexities Of Parallel Dft In MMmentioning

confidence: 99%

Fast Parallel Algorithm for Discrete Fourier Transform in Multi-Mesh Network

De¹,

Datta²,

Bhattacharya³

et al. 2014

Parallel and Distributed Computing and Networks

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“…These can be divided into two types, power-of-two and non-power-of-two. Certainly, the design of non-power-of-two FFT processors are more challenging because both data management and data processing is not regular [1]- [6].…”

Section: Introductionmentioning

confidence: 99%

Multiplierless unified architecture for mixed radix-2/3/4 FFTs

Qureshi

Takala

Volkova

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-This paper presents a novel runtime-reconfigurable, mixed radix core for computation 2−, 3−, 4− point fast Fourier transforms (FFT). The proposed architecture is based on radix-3 Wingorad Fourier transform, however multiplication is performed by constant multiplication instead of general multiplier. The complexity is equal to multiplierless 3-point FFT in terms of adders/subtractors with the exception of a few additional multiplexers. The proposed architecture supports all the FFT sizes which can be factorized into 2, 3, 4 point systems. We also show that the proposed architecture has the same bound on the accuracy as the classical one.

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Generation of all radix-2 fast Fourier transform algorithms using binary trees

Cited by 22 publications

References 8 publications

Low-Complexity Multiplierless Constant Rotators Based on Combined Coefficient Selection and Shift-and-Add Implementation (CCSSI)

Low-Complexity Multiplierless Constant Rotators Based on Combined Coefficient Selection and Shift-and-Add Implementation (CCSSI)

Fast Parallel Algorithm for Discrete Fourier Transform in Multi-Mesh Network

Multiplierless unified architecture for mixed radix-2/3/4 FFTs

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