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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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Patent
02 Aug 1999
TL;DR: In this paper, a transposeless 2-dimensional FFT with minimum number of clock cycles and minimum complexity is presented. But the complexity of the circuit is reduced by elimination of butterfly computation structure and adaptation of transpose-less 2D transform architecture.
Abstract: A circuit for performing Fast Fourier Transform (FFT) with minimum number of clock cycles and minimum complexity. One-dimensional FFT of size N=N 0 ×N 1 × . . . ×N M−1 , N m m=0, 1, . . . , M−1, positive numbers, is computed recursively, through a sequence of two-dimensional row-column transform computations of sizes, N 0 ×N 1 , (N 0 ×N 1 )×N 2 , (N 0 ×N 1 ×N 2 )×N 3 , . . . , (N 0 ×N 1 × . . . ×N M−2 )×N M−1 with twiddle factors. The complexity of the circuit is reduced by elimination of butterfly computation structure and adaptation of transposeless 2-D transform architecture.

13 citations

Proceedings ArticleDOI
R.J. Crinon1
08 May 1989
TL;DR: In this paper, a new interpolation scheme that allows the frequency and amplitude of a sinusoid to be estimated with high accuracy is proposed. But the method is based on the fact that spectral convolution introduces spectral leakage that can be observed at the output of an FFT.
Abstract: The problem with using the FFT to do spectral estimation is that only a sampled version of the discrete Fourier transform of the input signal is provided To do parameter estimation on a signal with frequency that does not appear at the output of the FFT, one has to perform spectral interpolation to approximate the original continuous spectrum The author introduces a new interpolation scheme that allows the frequency and amplitude of a sinusoid to be estimated with high accuracy The method is based on the fact that spectral convolution introduces spectral leakage that can be observed at the output of an FFT With the minimum four-sample Blackman-Harris window, this method yields better results than the conventional parabola-fitting technique The largest error occurs when the frequency is halfway between two frequency bins Higher-order Taylor series could be used to improve the estimation in the range of 045 >

13 citations

Journal ArticleDOI
TL;DR: In this paper, the Hartley transform is used to avoid the Hermitian symmetry of the complex-valued Fourier transform, which causes computational redundancies in terms of the number of operations and memory requirements.
Abstract: Phase‐shift migration techniques that attempt to account for lateral velocity variations make substantial use of the fast Fourier transform (FFT). Generally, the Hermitian symmetry of the complex‐valued Fourier transform causes computational redundancies in terms of the number of operations and memory requirements. In practice a combination of the FFT with the well‐known real‐to‐complex Fourier transform is often used to avoid such complications. As an alternative means to the Fourier transform, we introduce the inherently real‐valued, non‐symmetric Hartley transform into phase‐shift migration techniques. By this we automatically avoid the Hermitian symmetry resulting in an optimized algorithm that is comparable in efficiency to algorithms based on the real‐to‐complex FFT. We derive the phase‐shift operator in the Hartley domain for migration in two and three dimensions and formulate phase shift plus interpolation, split‐step migration, and split‐step double‐square‐root prestack migration in terms of the ...

13 citations

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: 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


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