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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: The RSB-DFT algorithm has the potential to become an alternative and efficient tool for sparse spectrum analysis and is demonstrated as the highest compared with the DFT, FFT, Goertzel algorithm.
Abstract: Discrete Fourier transform (DFT) is the basic means of spectrum analysis in the field of digital signal processing, and the fast Fourier transform (FFT) has become the most popular algorithm which decreases the computational complexity from quadratical to linearithmic. However, engineers are often challenged to detect a single or just a few of the frequency components. For this kind of sparse spectrum analysis, the FFT no longer has advantage because it always computes all the frequency components. This paper proposes a recursive single-bin DFT (RSB-DFT) algorithm to compute one specific frequency spectrum, whose theoretical derivation is elaborated and implementation steps are given as a flow diagram. A 16-point RSB-DFT calculation example is also given to exhibit computation process of the algorithm. An application example for bioimpedance spectroscopy (BIS) measurement demonstrates that the proposed RSB-DFT algorithm can compute specific single spectral lines accurately. The computation efficiency of the proposed RSB-DFT algorithm is demonstrated as the highest compared with the DFT, FFT, Goertzel algorithm, which means that the RSB-DFT algorithm has the potential to become an alternative and efficient tool for sparse spectrum analysis.
4 citations
TL;DR: An efficient solver for the three dimensional free-space Poisson equation is presented in this paper, where the underlying numerical method is based on finite Fourier series approximation while the error of all involved approximations can be fully controlled, the overall computation error is driven by the convergence of the finite-fraction series of the density for smooth and fastdecaying densities.
4 citations
TL;DR: This paper concentrates on the development of the Fast Fourier Transform (FFT) based on Decimation-In- Time (DIT) domain, Radix-2 algorithm, and uses VERILOG as a design entity.
Abstract: The Fast Fourier Transform (FFT) is one of the rudimentary operations in field of digital signal and image processing. Some of the applications of the fast Fourier transform include Signal analysis, Sound filtering, Data compression, Partial differential equations, Multiplication of large integers, Image filtering etc. Fast Fourier transform (FFT) is an efficient implementation of the discrete Fourier transform (DFT). This paper concentrates on the development of the Fast Fourier Transform (FFT), based on Decimation-In- Time (DIT) domain, Radix-2 algorithm, this paper uses VERILOG as a design entity. The input of Fast Fourier transform has been given by a keyboard using a test bench and output has been displayed using the waveforms on the Xilinx Design Suite 13.1 and synthesis results in Xilinx show that the computation for calculating the 32- point Fast Fourier transform is efficient in terms of speed. I. Introduction This proposes the design of 32-points FFT processing block. The work of the project is focused on the design and implementation of FFT for a FPGA kit. This design computes 32-points FFT and all the numbers follow fixed point format of the type Q8.23, signed type input format is used.The direct mathematical derivation method is used for this design. In this project the coding is done in VHDL (8) & the FPG synthesis and logic simulation is done using Xilinx ISE Design Suite 13.1. The Discrete Fourier Transform (DFT) plays an important role in the analyses, design and implementation of the discrete-time signal- processing algorithms and systems it is used to convert the samples in time domain to frequency domain. The Fast Fourier Transform (FFT) is simply a fast (computationally efficient) way to calculate the Discrete Fourier Transform (DFT). The wide usage of DFT"s in Digital Signal Processing applications is the motivation to Implement FFT"s. Almost every branch of engineering and science uses Fourier methods. The words "frequency," "period," "phase," and "spectrum" are important parts of an engineer's vocabulary.The Discrete Fourier transform is used to produce frequency analysis of discrete non periodic signals. The FFT is another method of achieving the same result, but with less overhead involved in the calculations. Fig1:
4 citations
25 Jun 2010
TL;DR: A novel 3780-point FFT algorithm for the China national broadcasting standard which adopts the pure PFA (prime factor algorithm) and nested Winograd FFT which can realize the identity in the circuit structure is proposed.
Abstract: This paper proposes a novel 3780-point FFT algorithm for the China national broadcasting standard. This new algorithm adopts the pure PFA (prime factor algorithm) and nested Winograd FFT which can realize the identity in the circuit structure. The simulation demonstrates that the new algorithm can achieve the equal accuracy rather than other methods but with the least quantity of multiplication.
4 citations
23 Mar 1992
TL;DR: An algorithm is presented which overcomes the problem for real symmetric and antisymmetric data sequences and a similar algorithm is given for the translational complex conjugate symmetric data sequence.
Abstract: A previously proposed algorithm for the FFT (fast Fourier transform) computation of real symmetric and antisymmetric sequences reduced the N-point symmetric FFT computation to a N/4-point complex FFT computation, but the postprocessing involved division by sin(2 pi k/N). For large size N, this may cause stability problems. An algorithm is presented which overcomes the problem for real symmetric and antisymmetric data sequences. A similar algorithm is given for the translational complex conjugate symmetric data sequence. >
4 citations