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.

On the derivation of the fast Fourier transform

Abstract: The fast Fourier transform (FFT) provides an effective tool for the calculation of Fourier transforms involving a large number of data points. The paper presents new and simple derivations for the two basic FFT algorithms that provide an intuitive basis for the manipulations involved. The derivation for the "decimation in time" algorithm begins with a crude analysis for the zero frequency and fundamental components using only two data samples, one at the beginning and the second at the midpoint of the period of interest. Successive interpolations of data points midway between those previously used result in a refinement of the amplitudes already determined and a first value for the next higher order coefficients. The derivation of the "decimation in frequency" algorithm begins by resolving the original data set into two new data sets, one whose transform includes only even harmonic terms and a second whose transform includes only odd harmonic terms. Since the first of the two new data sets repeats after the midpoint, it can be transformed using only the first half of the data points. The second of the new data sets is multiplied by the negative fundamental function, thereby reducing its order by one and converting it into a data set that transforms into even harmonics only; in this form it can also be transformed using only the first half of the data set. Successive applications of this procedure result finally in reducing the operation to the calculation of a large number of simple two-data-point transforms.

Magnitude-only reconstruction of two-dimensional sequences with finite regions of support

Abstract: In this paper, a conceptual algorithm for reconstructing a two-dimensional (2-D) complex-valued finite sequence from an adequate set of samples of the magnitude of its Fourier transform is presented. In particular, one obtains, at least theoretically, all solutions of the 2-D magnitude-only reconstruction problem, provided that the modulus of the DFT is available in a sufficiently large set of points. However, the practicability of this algorithm is limited to sequences with relatively small regions of support. The key for developing the method is shown to be an appropriate mapping of 2-D finite sequences into 1-D ones, such that 2-D discrete correlation can be formulated in terms of ordinary 1-D discrete correlation.

New FFT structures based on the Bruun algorithm

Abstract: In some signal processing applications, the input data are real. In this case, the Bruun algorithm for computation of the discrete Fourier transform (DFT) is attractive. The author offers a pipeline and a recirculated shuffle network implementation of the Bruun algorithm. The implementation of the parallel pipeline and recirculated FFT structures is based on the modified perfect shuffle network. >

Ram-based fast fourier transform unit for wireless communications

Abstract: A wireless communication technique enables fast Fourier transforms (FFTs) and inverse fast Fourier transforms (IFFTs) to be performed with reduced latency and reduced memory requirements. In particular, an FFT/IFFT unit receives input data representative of a communication symbol. The FFT/IFFT unit applies an FFT operation to the input data to generate intermediate data. The FFT/IFFT unit stores the intermediate data in a random access memory (RAM). The intermediate data stored in the RAM may override data used as input to the FFT operation. The FFT/IFFT unit selectively addresses the RAM to retrieve the intermediate data in a desired output order. For example, the FFT/IFFT unit may output the intermediate data in the same sequential order as the FFT/IFFT unit received the input data.