Showing papers on "Rader's FFT algorithm published in 1992"

Generalized discrete Hartley transforms

Abstract: The discrete Hartley transform is generalized into four classes in the same way as the generalized discrete Fourier transform. Fast algorithms for the resulting transforms are derived. The generalized transforms are expected to be useful in applications such as digital filter banks, fast computation of the discrete Hartley transform for any composite number of data points, fast computations of convolution, and signal representation. The fast computation of skew-circular convolution by the generalized transforms for any composite number of data points is discussed in detail. >

Split vector-radix fast Fourier transform

Abstract: The split-radix approach for computing the discrete Fourier transform (DFT) is extended for the vector-radix fast Fourier transform (FFT) to two and higher dimensions. It is obtained by further splitting the (N/2*N/2) transforms with twiddle factors in the radix (2*2) FFT algorithm. The generalization of this split vector-radix FFT algorithm to higher radices and higher dimensions is also presented. By introducing a general approach for constructing the fast Hartley transform (FHT) from the corresponding FFT, new vector- and split-vector-radix FHT algorithms with the same desirable properties as their FFT counterparts are obtained. >

A generalized prime factor FFT algorithm for any N=2 p 3 q 5 r

Abstract: Prime factor fast Fourier transform (FFT) algorithms have two important advantages: they can be simultaneously self-sorting and in-place, and they have a lower operation count than conventional FFT algorithms. The major disadvantage of the prime factor FFT has been that it was only applicable to a limited set of values of the transform length N. This paper presents a generalized prime factor FFT, which is applicable for any $N = 2^p 3^q 5^r $, while maintaining both the self-sorting in-place capability and the lower operation count. Timing experiments on the Cray Y-MP demonstrate the advantages of the new algorithm.

An optimal multiplication algorithm for reconfigurable mesh

Abstract: It is shown that multiplication of two N-bit integers can be performed in O(1) time on N*N reconfigurable mesh. This result is obtained by combining the O(1) time multiplication algorithm on N*N/sup 2/ reconfigurable mesh, the Rader transform, and decomposition of one-dimensional convolution into multidimensional convolution. Choosing the Radar transform at the expense of long word length frees one from storing twiddle factors in advance, which is needed in other designs. It is also shown that the present algorithm can be simulated on other restricted reconfigurable mesh models without asymptotic increase in time or number of processing elements. It is shown that the present result can be extended to provide area-time tradeoffs in the usual bit model of VLSI to satisfy AT/sup 2/ optimality over 1 >

A prime factor fast W transform algorithm

Abstract: A method for converting any nesting DFT algorithm to the type-I discrete W transform (DWT-I) is introduced. A nesting algorithm that differs from either the Windograd Fourier transform algorithm (WFTA) or the prime factor FFT algorithm (PFA) is presented. New small-N DETs, which are suitable for this nesting algorithm, are developed based on using sparse matrix decomposition. The proposed algorithm is more efficient that either WFTA or PFA for large N, and it is more flexible for the choice of transform length, because 32 points are used. For 2D processing, the proposed algorithm is more efficient than the polynomial transform. >

High speed multidimensional systolic arrays for discrete Fourier transform

Abstract: An efficient algorithm that places an optimized DG (dependence graph) for 2/sup n/ points of the discrete Fourier transform (DFT) computation is proposed. A one-dimensional DFT is turned into a multidimensional DFT, consisting of a few short DFTs, which is based on the version of the Goertzel algorithm via Horner's rule. The data sequences in the Cooley-Tukey FFT algorithm are in an order that is easily manageable and well suited for vector processors and any parallel machine such as hypercube. >

An efficient FFT algorithm for real-symmetric data

Abstract: A very efficient algorithm for computing the discrete Fourier transform (DFT) of real-symmetric input is presented. The algorithm is based on Bruun's algorithm where, except for the last stage, all twiddle factors are purely real. It is well-known that about half of the arithmetic operations and memory requirements can be removed when the input is real-valued. It may be assumed that another half of the computational and memory requirements can be eliminated when the input is real and symmetric. This is, however, impossible with a standard radix-2 fast Fourier transform (FFT), but can be achieved by the Bruun algorithm. The symmetries within the algorithm with for real-symmetric input are exploited to remove about three fourths of the butterflies and memory locations. The algorithm presented achieves the same low arithmetic as the split-radix FFT for real-symmetric data, but has a structure that is as simple as the radix-2. The implementation on the TMS320C30 shows that the new algorithm fits a DSP processor very well. The program requires 0.51-0.60 ms to compute a length 1024 FFT with real-symmetric data. >

Fast 2D convolution filter based on look up table FFT

Abstract: This paper shows a fast implementation method of a two dimensional (2D) filter. The filter design is based on fast convolution related to the fast Fourier transform (FFT) look up table. This is then extended to the 2D FFT. The design and implementation of the system gives a good accurate selection of the desired frequency. The system has a step advantage of a reduction in the operation time. >

Automating the design of prime length FFT programs

Abstract: The automatic design of prime-length fast Fourier transforms (FFTs) based on S. Winograd's (1980) theory is described. A program is described that generates code for FFTs so that longer prime length FFTs that were formerly practical to design are now easily generated. For those prime lengths ( >

A novel correlation‐based FFT algorithm

Abstract: Since the discovery of the fast Fourier transform (FFT), many new FFT algorithms have been developed. Conventionally, the convolution‐based approach deals commonly with the prime length discrete Fourier transforms. In this paper, based on some theorems of Number Theory, a new algorithm for computing the FFT (with power of two length) is proposed. This novel recursive algorithm contains three stages, the first and the last stages contain only additions and substractions, and the second stage is of block diagonal form, with each block being a circular correlation/convolution matrix. The newly proposed convolution‐based FFT algorithm has the following advantages: 1. In terms of computational counts, this algorithm can achieve the multiplicative lower bound derived by Winograd. 2. The proposed algorithm can easily be implemented in a parallel computing environment. 3. The proposed algorithm is recursive in nature, and thus the computation structure is rather regular.

Development and simulation of a 4080-point Winograd fast Fourier transform processor

Abstract: By using the Good-Thomas prime factor algorithm, 15-, 16-, and 17-point Winograd algorithm fast Fourier transform (FFT) processors are combined to perform 4080-point FFTs. The circuits are analyzed in VHSIC hardware description language (VHDL), simulated, and laid out in MAGIC for fabrication through MOSIS. The VHDL simulation includes behavioral modeling and the simulation of 15-, 16-, 17-, and 4080-point FFT problems. Two of the three FFT processors are submitted for fabrication using a 1.2- mu m CMOS process. >