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.

Efficient linear equalization for high data rate downlink CDMA signaling

Abstract: In this paper, we propose an FFT-based linear equalization algorithm for the CDMA downlink. By approximating the correlation matrix with a circulant matrix, which is diagonalized by the DFT matrix, we are able to incorporate the efficient FFT operations and avoid the direct matrix inversion. Furthermore, we show that with the help of Kronecker algebra and the notion of dimension-wise and element-wise FFT, we are able to extend the FFT-based method to cases where multi-channel diversity, such as over-sampling or receive antenna array diversity, is present. Numerical simulations show that the FFT-based algorithm overlaps with the direct matrix inversion method for most of the low to medium SNR range and have a small loss at high SNR.

Constant geometry algorithm for discrete cosine transform

Abstract: Modification to the architecture-oriented fast algorithm for discrete cosine transform of type II from Astola and Akopian (see ibid., vol.47, no.4, p.1109-24, April 1999) is presented, which results in a constant geometry algorithm with simplified parameterized node structure. Although the proposed algorithm does not reach the theoretical lower bound for the number of multiplications, the algorithm possesses the regular structure of the Cooley-Tukey FFT algorithms. Therefore, the FFT implementation principles can also be applied to the discrete cosine transform.

The quick Fourier transform: an FFT based on symmetries

Abstract: This paper looks at an approach that uses symmetric properties of the basis function to remove redundancies in the calculation of the discrete Fourier transform (DFT). We develop an algorithm called the quick Fourier transform (QFT) that reduces the number of floating-point operations necessary to compute the DFT by a factor of two or four over direct methods or Goertzel's method for prime lengths. By further application of the idea to the calculation of a DFT of length-2/sup M/, we construct a new O(NlogN) algorithm, with computational complexities comparable to the Cooley-Tukey algorithm. We show that the power-of-two QFT can be implemented in terms of discrete sine and cosine transforms. The algorithm can be easily modified to compute the DFT with only a subset of either input or output points and reduces by nearly half the number of operations when the data are real.

High-resolution narrow-band spectra by FFT pruning

Abstract: A new method of computing high-resolution narrow-band spectra faster than the chirp z transform (CZT) and direct computation of discrete Fourier transform (DFT) is presented. This is achieved by a generalization of Markel's pruning algorithm and in combination with Skinner's pruning algorithm for the decimation-in-time FFT formulation. However, for very high resolutions it is shown that the CZT is selectively superior to the new method.

Pipelined, high-precision fast fourier transform processor

Abstract: The Fast Fourier Transform (FFT) processor includes a plurality of pipelined, functionally identical stages, each stage adapted to perform a portion of an FFT operation on a block of data. The output of the last stage of the processor is the high-precision Fast Fourier Transform of the data block. Support functions are included at each stage. Thus, each stage includes a computational element and a buffer memory interface. Each stage also includes apparatus for coefficient generation.