Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.

Pipeline processor for fast architecture oriented regular DCT-IDCT algorithm

Abstract: New architecture oriented regular algorithms are proposed for the discrete cosine transform (DCT), used in DSP problems, with a simple data shuffling pattern similar to the Cooley-Tukey FFT algorithm. One can easily extend many of parallel FFT approaches for these algorithms. The only pipeline structure with logN-1 arithmetic units and transform time of order O(N) is considered. It is simpler than the known pipeline structures.

Chinese chess recognition based on log-polar transform and FFT

Abstract: In this paper, we present a new method for recognizing Chinese chess. Firstly, histogram equalization and Hough gradient transform is used to determining the location of chess center; Secondly, Log-Polar Transform is used to achieve rotation-invariant and scale-invariant after preprocessing; Thirdly, Fast Fourier Transform (FFT) can achieve translation-invariant. A simple measurement is used to assess the similarity after horizontal and vertical projection. Experiment results have shown that the algorithm can effectively recognize all chesses.

A modified FFT-based algorithm for real-time computation of discrete wavelet transform

Abstract: In this paper, an efficient FFT-based algorithm is proposed for fast computation of discrete wavelet transform (DWT). By virtue of the Fourier-space operations, significant saving in computational complexity is achieved. The Fourier-domain subsampling results in single IFFT operation at the intermediate level thus reducing the computational burden. The Fourier-domain subsampling and the Hermitian symmetry property of the Fourier-transform of a real function provides significant reduction in overall computations. The comparison of the computational complexity of an FFT-based fast wavelet transform (FWT) algorithm with the proposed algorithm for various cases of decomposition levels and wavelet kernel size is done. We found that the proposed algorithm reduces the number of multiplications per point by 22% and by 35% in the case of additions for 'db8' wavelet at a of five. This gain is of practical interest in computationally intensive applications.

FFT optimization algorithm and realization of MATLAB

Abstract: In order to realize the FFT algorithm more flexibly and effectively, this paper analyzed four kinds of amplitude spectrum or power spectrum correction methods, that is, ratio correction method, energy centrobaric correction method, phase difference method and FFT + FT spectrum analysis method. On this basis, a double-window function spectrum estimation algorithm was introduced, which was a kind of conjoint analysis algorithm with rectangular window function and improved window function. The algorithm could improve the amplitude estimation accuracy in the case of not reducing the frequency resolution. The effectiveness of this algorithm was proved by using MATLAB software. The simulation results show that the double-window function spectrum estimation algorithm significantly decreases the amplitude estimation error brought by the picket fence effect, and realizes the optimization of FFT algorithm.

The Empirical Mode Decomposition algorithm via Fast Fourier Transform

Abstract: In this paper we consider a problem of implementing a fast algorithm for the Empirical Mode Decomposition (EMD). EMD is one of the newest methods for decomposition of non-linear and non-stationary signals. A basis of EMD is formed "on-the-fly", i.e. it depends from a distribution of the signal and not given a priori in contrast on cases Fourier Transform (FT) or Wavelet Transform (WT). The EMD requires interpolating of local extrema sets of signal to find upper and lower envelopes. The data interpolation on an irregular lattice is a very low-performance procedure. A classical description of EMD by Huang suggests doing this through splines, i.e. through solving of a system of equations. Existence of a fast algorithm is the main advantage of the FT. A simple description of an algorithm in terms of Fast Fourier Transform (FFT) is a standard practice to reduce operation's count. We offer a fast implementation of EMD (FEMD) through FFT and some other cost-efficient algorithms. Basic two-stage interpolation algorithm for EMD is composed of a Upscale procedure through FFT and Downscale procedure through a selection procedure for signal's points. First we consider the local maxima (or minima) set without reference to the axis OX, i.e. on a regular lattice. The Upscale through the FFT change the signal’s length to the Least Common Multiple (LCM) value of all distances between neighboring extremes on the axis OX. If the LCM value is too large then it is necessary to limit local set of extrema. In this case it is an analog of the spline interpolation. A demo for FEMD in noise reduction task for OCT has been shown.