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.

An improved fast algorithm for chirp transforms and its applications

Abstract: A fast algorithm for chirp Z-transforms is improved form chirp Z-transform, which is developed by using two fast Fourier transforms and an analytical Gaussian kernel. Its computational complexity is less than a fast convolution algorithm. However, there are some problems when the algorithm is implemented, such as the discarding of the data, the smallness of the response domain, the bigness of the computational complexity and so on. To avoid the problems mentioned above, we make a change on the implementing of the algorithm in this paper. Then we compare the numerical results of some chirp systems with the analytical ones. The accuracy of Fourier transforms of Gaussian function is higher than the 10 -15 order for most cases, and the accuracy of Fourier transforms of rectangle function is about the 10 -3 order, which is essentially limited by the accuracy of the fast Fourier transform. Finially this algorithm is used to calculate some typical systems of scalar diffraction and fractional-order Fourier transforms, and the results are in good agreement with other published results in the literatures.

A More Accurate Fourier Transform

Abstract: Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods oer speed advantages over evaluation of explicit integrals (EI) that dene Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric CO2 concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT’s FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability to compute more accurate Fourier transforms has promise for improved data analysis in many elds, including more sensitive assessment of hypotheses in the environmental sciences related to CO2 concentrations and temperature. Other methods are available to address dierent weaknesses in FFTs; however, the EI method always produces the most accurate output possible for a given data set. On the 2011 Lenovo ThinkPad used in this study, an EI transform on a 10,000 point data set took 31 seconds to complete. Source code (C) and Windows executable for the EI method are available at https://sourceforge.net/projects/amoreaccuratefouriertransform/.

A two-dimensional discrete convolution algorithm

Abstract: A theoretical result concerning the discrete Fourier transform is derived and used to develop a transform algorithm for computing two-dimensional convolutions. The use of this algorithm minimises the number of arithmetic operations and the memory requirements in computing a convolution of order (M×N) using a transform processor or program designed for a length No, where M≤N0 and N≤N0.It is particularly suitable for computing convolutions whose orders are not powers of two using conventional fast Fourier transform processors. Methods of implementing the algorithm are also presented.

Improved fast polar Fourier transform algorithm

Abstract: The problem of calculating the discrete Fourier tranform (DFT) acquired in polar coordinate system has been given considerably attention in many fields such as antenna, image registration and tomography. This paper proposes an improved fast DPFT algorithm aiming at 2D real data. In this paper, a Conjugated-like property of the conjugated sequences' Chirp-Z transform (CZT) in symmetric frequency section is proved which saves half of the computational complexity in CZT. The algorithm is suitable for real-time applications by only 1D calcuations in which the most steps are 1D FFT. The experimental results show the applicability and good performance of this approach.