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.

Time-Domain Processing of Frequency-Domain Data and Its Application

Abstract: Based on our previous work, this work presents a complete method for time-domain processing of frequency-domain data with evenly-spaced frequency indices, together with its application. The proposed method can be used to calculate the cross spectral and power spectral densities for the frequency indices of interest. A promising application for the time-domain processing of frequency-domain data, particularly for calculating the summation of frequency-domain cross- and auto-correlations in orthogonal frequency-division multiplexing (OFDM) systems, is studied. The advantages of the time-domain processing of frequency-domain data are 1) the ability to rapidly acquire the properties that are readily available in the frequency domain and 2) the reduced complexity. The proposed fast algorithm directly employs time-domain samples, and hence, does not need the fast Fourier transform (FFT) operation. The proposed algorithm has a lower complexity (required complex multiplications ∼ O(N)) than conventional techniques.

A Fast Algorithm With Less Operations for Length- DFTs

Abstract: Discrete Fourier transform (DFT)iswidelyusedinal- most all fields of science and engineering. Fast Fourier transform (FFT) is an efficient tool for computing DFT. In this paper, we present a fast Fourier transform (FFT) algorithm for computing length- DFTs. The algorithm transforms all -points sub- DFTs into three parts. In the second part, the operations of sub- transformation contain only multiplications by real constant fac- tors. By transformation, length- -scaled DFTs (SDFT) are ob- tained. An extension of scaled radix-2/8 FFT (SR28FFT) is pre- sented for computing these SDFTs, in which, the real constant fac- tors of SDFTs are attached to the coefficients of sub-DFTs to sim- plify multiplication operations. The proposed algorithm achieves reduction of arithmetic complexity over the related algorithms. It can achieve a further reduction of arithmetic complexity for com- puting a length- IDFT by

The direct application of FFT algorithms on the synthesis of non-uniformly spaced arrays

Abstract: In previous work, we presented one efficient method applying the FFT (Fast Fourier Transform) algorithms to the computation of non-uniformly spaced antenna array factors, based on the Fourier relation between the array factor and its source distribution. Using the grid in the spatial domain, the element positions of one non-uniformly spaced array are set to another equi-spaced array with the smaller spacing. Then, the conventional IFFT (Inverse FFT) algorithm is used to compute its array factor. According to the reciprocal property of the Fourier transform, the direct Fourier transform can be applied in the synthesis problem of non-uniformly spaced arrays. If the array factor of one non-uniformly spaced array is completely given in the respective region, the correspondent array excitation can be obtained by directly applying the FFT after using the sampling theorem. If it is not, the synthesized array will not be exactly as desired after directly applying the FFT algorithm. In this case, the array element positions are chosen to be those where the array element distribution is concentrated. To achieve the more approximated array factor, we can use some methods to modify the array element currents, for example, the matrix relation between the array factor samples and the array element currents. Thus, in this paper we show the possibility of the FFT algorithm application directly in the synthesis of non-uniformly spaced arrays and demonstrate how to synthesize one non-uniformly spaced array from the samples of array factors under the Fourier relation. Of course, this method can also be used in the synthesis of uniformly spaced arrays, which is viewed as the particular problem. Due to the application of the FFT algorithm, the advantages such as fast computation, easy use and so on are obvious. Furthermore, this method permits the exact array source distribution of a non-uniformly spaced array to be obtained, given the corresponding array factor.

Pseudo-Spectral Method

Abstract: This chapter elaborates about pseudo-spectral method applicable to most commonly hyperbolic equations with periodic boundary conditions. A numerical scheme for calculating the spatial derivatives is obtained. A numerical finite Fourier transform (FFT)can be used to obtain difference schemes that are of infinite order. Methods of arbitrary high order may be constructed. For higher order methods, more points surrounding the point x k will be utilized. The fast Fourier transforms is a fast numerical technique for determining the FFT of a function that is defined on a set of equally spaced grid points. The derivative at every point in the grid can be computed by taking an FFT, multiplying by the discrete analogue of iω , and then taking an inverse FFT.

Realization of a discrete Fourier transform (DFT) module for incorporation in FFT processors

Abstract: For applications requiring high-speed and in-place treatment, it is often advantageous to realize special-purpose computers. This paper describes a discrete Fourier transform (DFT) module for incorpration in fast Fourier transform (FFT) processors. The module is highly suitable for real input applications requiring high-speed transformations. It attributes one point to all frequency channels in one clock cycle. This treatment is not only well suited for the present technology, but appears to be more attractive in view of recent trends in digital circuitry.