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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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TL;DR: QDFT and quantum convolution demonstrate that quantum signal processing with classical output is possible and time complexity O(sqrt(N)) and O(N) respectively.
Abstract: Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms with classical output (1D QDFT and 2D QDFT) are presented in this paper. And quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, QDFT has two advantages at least. One of advantages is that 1D and 2D QDFT has time complexity O(sqrt(N)) and O(N) respectively. The other advantage is that QDFT can process very long signal sequence at a time. QDFT and quantum convolution demonstrate that quantum signal processing with classical output is possible.

5 citations

Journal ArticleDOI
TL;DR: It can be proved that the computational complexity of the proposed DFT algorithm is identical to that of the most popular split-radix FFT, yet requires real number arithmetics only.
Abstract: Discrete Fourier transform (DFT)/discrete Hartley transform (DHT) algorithms based on the basis-vector decomposition of the corresponding transform matrices are derived. The computations of DFT are divided into two stages: an add/subtract preprocessing and a block-diagonal postprocessing. Both stages can be computed effectively. It can be proved that the computational complexity of the proposed DFT algorithm is identical to that of the most popular split-radix FFT, yet requires real number arithmetics only. Generation and storage of the real multiplicative coefficients are easier than that in conventional FFTs. Connections of the proposed approach with several well-known DFT algorithms are included. Furthermore, many variations of the proposed algorithm are also pointed out. >

5 citations

Patent
Ho-Jung Kim1, Hoon Song1, Hong-Seok Lee1
25 Jul 2016
TL;DR: In this article, a method of performing a Fourier transform on data having rows and columns, in a row direction, and storing a portion of the second data in a column direction is presented.
Abstract: A method of performing a Fourier transform includes generating first data by performing a one-dimensional (1D) fast Fourier transform (FFT), on data having rows and columns, in a row direction; generating second data by performing the 1D FFT, on a portion of the first data, in a column direction; and storing a portion of the second data.

5 citations

Proceedings ArticleDOI
02 Jun 2011
TL;DR: The designed FFT/IFFT ASIC chip, based on iterative radix-2 decimation in frequency (DIF) algorithm, is very much suitable for low-area and low power biomedical applications like CT image reconstruction, Doppler wave spectrogram etc.
Abstract: The CT scan medical imaging requires huge amount of computations for reconstructing the images. Modified Fast Radon Transform (MFRT) uses FFT based parallel algorithm for reconstruction of 2D/3D CT images from its sonogram data using convolution operation by concurrent 1D FFT/IFFT and matrix multiplications. To achieve optimum hardware utilization with low power consumption an FFT module, based on iterative radix-2 decimation in frequency (DIF) algorithm, has been designed and implemented. The module has been designed in such way so that it can also be used for IFFT computation only by changing a single parameter. To compute the FFT, the twiddle factor has been calculated using Coordinate Rotation Digital Computer (CORDIC), by steering the data properly in the butterfly structure. The synthesized frequency of FFT/IFFT module is 220 MHz and gate count is 1,040,136 using 130 nm faraday digital libraries. The power has been analyzed using prime power and the value of the power consumption is 15mW. The designed FFT/IFFT ASIC chip is very much suitable for low-area and low power biomedical applications like CT image reconstruction, Doppler wave spectrogram etc.

5 citations

Journal ArticleDOI
TL;DR: Two new numerical algorithms based on the Fast Fourier Transform techniques (FFT) are used to solve the structured robustness analysis problem in the case of one parameter entering polynomially (Barmish, 1994).

5 citations


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