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Split-radix FFT algorithm

About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.


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Proceedings ArticleDOI
25 Sep 2014
TL;DR: This paper introduces a restructure of the butterflies of the radix-2 FFT to be more CORDIC friendly, which achieves superior signal to quantization noise ratio (SQNR), and leads to an improvement in latency or a reduction in the total area.
Abstract: Fast Fourier Transform (FFT) is one of the basic building blocks in signal processing and communications systems. The butterflies-based structure of the FFT is the main reason for the reduced number of arithmetic operations required to implement the transform. From implementation point of view, the complex rotations used in butterflies can be implemented by using COordinate Rotation DIgital Computer (CORDIC). This implementation strategy reduces the hardware complexity compared to the direct implementation of the butterflies using complex multipliers. In this paper, we introduce a restructure of the butterflies of the radix-2 FFT to be more CORDIC friendly. This algorithm-level modification of the FFT is friendly towards all CORDIC types, including those introducing non-fixed gain. Compared with the conventional radix-2 FFT algorithm, the proposed algorithm introduces a substantial increase in performance. For example, it achieves superior signal to quantization noise ratio (SQNR), with around 14 dB gain for 8 to 1024 points FFT. In addition, in pipeline architectures the modification leads to an improvement in latency or a reduction in the total area, with an improvement in either of 38% for 1024 points FFT.

13 citations

Proceedings ArticleDOI
25 May 2003
TL;DR: An efficient split-radix FFT algorithm is proposed for computing the length-2/sup r/ DFT that reduces significantly the number of data transfers, index generations, and twiddle factor evaluations or accesses to the lookup table.
Abstract: In this paper, an efficient split-radix FFT algorithm is proposed for computing the length-2/sup r/ DFT that reduces significantly the number of data transfers, index generations, and twiddle factor evaluations or accesses to the lookup table. It is shown that the arithmetic complexity of the proposed algorithm is no more than that of the existing split-radix algorithm. The basic idea behind the proposed algorithm is that a radix-2 and a radix-8 index maps are used instead of a radix-2 and a radix-4 index maps as in the classical split-radix FFT. In addition, since the algorithm is expressed in a simple matrix form using the Kronecker product, it facilitates an easy implementation of the algorithm, and allows for an extension to the multidimensional case.

12 citations

Journal ArticleDOI
TL;DR: The technique is capable of reducing the memory requirement by a factor of 6/spl sim/16 depending on the number of modes used and the spatial distribution of scatterers and is simple to implement in an existing FFT T-matrix code.
Abstract: We present a memory-reduction technique for the fast Fourier transformation (FFT) T-matrix method. The technique exploits the configuration- and Fourier-space symmetry relations of the transverse spherical multipole translation coefficients whose storage drives the memory requirement. The technique is capable of reducing the memory requirement by a factor of 6/spl sim/16 depending on the number of modes used and the spatial distribution of scatterers and is simple to implement in an existing FFT T-matrix code. We establish its accuracy and effectiveness by applying the technique to compute the RCS of aggregates of dielectric spheres.

12 citations

Proceedings ArticleDOI
30 May 1994
TL;DR: In this paper the sliding implementation of the other useful transforms, that can also be implemented with the order of N complexity, are worked out in detail.
Abstract: Implementation of the transform domain adaptive filters is addressed. Recent results have shown that if the input data to a radix-2 fast Fourier transform (FFT) structure is sliding one sample at a time, only N-1 butterflies need to be calculated for updating the FFT structure, after the arrival of every new data sample. This is opposed to most of the previous reports that, assume order of N log N complexity, for such implementation. In this paper the sliding implementation of the other useful transforms, that can also be implemented with the order of N complexity, are worked out in detail. >

12 citations

Patent
02 Jan 1998
TL;DR: In this paper, a method and apparatus for calculating fast Fourier transforms FFTs are described, and a tensor product based implementation of the FFT of a given size is presented.
Abstract: A method and apparatus for calculating fast Fourier transforms FFTs are disclosed. An FFT of a given size is formatted using tensor product principles for implementation in apparatus or by software such that the same reconfigurable hardware or software can calculate FFTs of any dimension for the selected FFT size. The FFT is factored and presented to a first permutation block (10), then to first computation blocks (12, 14, 16, 18) for computing tensor products of dimensionless Fourier transforms of a relatively small base size and twiddle factors, then to a second permutation block (20), then to second computation blocks (22, 24, 26, 28), and finally to a third permutation block (30). The basic building blocks (10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30) of the circuitry can be reconfigurable for maximizing use-flexibility of the hardware or software.

12 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20239
202234
20192
20188
201748
201689