Showing papers on "Split-radix FFT algorithm published in 1986"

Implementation of "Split-radix" FFT algorithms for complex, real, and real-symmetric data

Abstract: A new algorithm is presented for the fast computation of the discrete Fourier transform. This algorithm belongs to that class of recently proposed 2n-FFT's which present the same arithmetic complexity (the lowest among any previously published one). Moreover, this algorithm has the advantage of being performed "in-place," by repetitive use of a "butterfly"-type structure, without any data reordering inside the algorithm. Furthermore, it can easily be applied to real and real-symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm.

On computing the split-radix FFT

Abstract: This paper presents an efficient Fortran program that computes the Duhamel-Hollmann split-radix FFT. An indexing scheme is used that gives a three-loop structure for the split-radix FFT that is very similar to the conventional Cooley-Tukey FFT. Both a decimation-in-frequency and a decimation-in-time program are presented. An arithmetic analysis is made to compare the operation count of the Cooley-Tukey FFT fo several different radixes to that of the split-radix FFT. The split-radix FFT seems to require the least total arithmetic of any power-of-two DFT algorithm.

A new FFT algorithm of radix 3,6, and 12

Abstract: A new algorithm for implementation of radix 3, 6, and 12 FFT is introduced. An FFT using this algorithm is computed in an ordinary (1,j) complex plane and the number of additions can be significantly reduced; the number of multiplication is also reduced. High efficiency of the algorithm is derived from the fact that, if an input sequence is favorably reordered, rotating factors can be treated in pairs so that the rotating factors are conjugate to each other.

Implementation of FFT structures using the residue number system

Abstract: This paper considers the implementation of a fast Fourier transform (FFT) structure using arrays of read-only memories. The arithmetic operations are based entirely on the residue number system. The most important aspect of the structure relates to the scaling arrays, which are required to prevent overflow. Because of the limitations of the number system, scaling factors have to be chosen on an a priori basis. This paper develops optimum procedures for choosing both scaling factors and the position of scaling arrays in the structure. Some examples are presented relating to the filtering of speech via a convolutional filter structure.

Pruning the decimation-in-time FFT algorithm with frequency shift

Abstract: Fourier transformed components within desired narrow-band can be efficiently calculated by the pruned version of the decimation-in-time FFT algorithm. A new pruning method is proposed here which invloves frequency shift. The shifting simplifies the pruning algorithm because its flowgraph has a repetitive pattern of butterflies between adjacent stages.

Conversion of FFT's to Fast Hartley Transforms

Abstract: The complex Fourier transform of a real function and its real Hartley transform are expressed in terms of each other, allowing translation of theorems and computer programs between the two versionsAny FFT can thus be converted, by a few indexing changes, into a Fast Hartley Transform which is equally efficient, in terms of floating point operations per real datum transformed The FHT can therefore transform one real array of length N in half the time that it takes the FFT to process a complex array of length N Several tricks to speed up both FHT and FFT are presented and a Fortran version of the FHT is supplied which delivers the result in $75\log _2 N$ multiplications and $175\log _2 N$ additions

Computing the complete fft of a step-like waveform

Abstract: Methods for duration limiting a step-like waveform for fast Fourier transform (FFT) computation are surveyed and discussed, and a complete FFT method is introduced. The complete FFT has an enhanced resolution, and is complete in the sense that it has uniformly spaced DC and harmonic components.

Easy generation of small-Ndiscrete Fourier transform algorithms

Abstract: In the paper, a set of rules is provided that allow construction of a wide range of efficient Rader's discrete Fourier transform (DFT) algorithms for the sizes of N being (a power of) an odd prime, having a limited set of polynomial reduction, multiplication and reconstruction algorithms. In theory, the algorithms obtained meet the lower bound on the number of multiplications. In practice, they have the same performance as the existing ones, and some new interesting algorithms are obtained, in particular for N = 25 and 27. For N being a power of 2, the use of the radix-4/2 fast Fourier transform is proposed, as this algorithm exhibits excellent properties when used as a small-N DFT algorithm. The paper contains two results of more general application: a rule determining when to use nesting or row-column algorithms, and propositions of new bounds on the number of multiplications for DFT algorithms for N = Pr, where p is a prime number.

Fast Fourier transform data address pre-scrambler circuit

Abstract: A fast Fourier transform (FFT) data address pre-scrambler technique and cuit for selectively generating pre-scrambled bit reversed, data address sequences needed to perform radix-2, radix-4 and mixed radix-2/4 fast Fourier transforms.

An efficient vector implementation of the FFT algorithm on IBM 3090VF

Abstract: In this paper, an efficient vector implementation of the fast Fourier transform (FFT) algorithm on the IBM 3090 Vector Facility is presented. This is a part of the Engineering and and Scientific Subroutine Library (ESSL). The implementation works with the full vector length of the machine and the cache is also efficiently managed to achieve very good performance. For short length transforms, a multiple number of transforms could be computed to improve performance. The performance of the vector rountines is compared against state of the art scalar routines and the performance improvements of up to a factor of 8 are observed.

VLSI Implementation Of The Fast Fourier Transform

Abstract: A VLSI implementation of a Fast Fourier Transform (FFT) processor consisting of a mesh interconnection of complex floating-point butterfly units is presented. The Cooley-Tukey radix-2 Decimation-In-Frequency (DIF) formulation of the FFT was chosen since it offered the best overall compromise between the need for fast and efficient algorithmic computation and the need for a structure amenable to VLSI layout. Thus the VLSI implementation is modular, regular, expandable to various problem sizes and has a simple systolic flow of data and control. To evaluate the FFT architecture, VLSI area-time complexity concepts are used, but are now adapted to a complex floating-point number system rather than the usual integer ring representation. We show by our construction that the Thompson area-time optimum bound for the VLSI computation of an N-point FFT, area-time2oc = ORNlogN)1+a] can be attained by an alternative number representation, and hence the theoretical bound is a tight bound regardless of number system representation.

Accumulation of product roundoff errors in modified FFT's

Abstract: In this paper, expressions are derived for the mean square error in modified radix-2 FFT algorithms. To reduce the mean square error at the output of a special purpose, high-speed low-order (n {\leq} 32) FFT processor implemented in fixed-point arithmetic, a modified FFT architecture is considered in which an extra bit is added to the register wordlength to prevent overflow. In this way, the scaling error is avoided and only the error due to product roundoff remains, in the case of implementation with stored-product ROM multipliers. The predicted signal/noise ratios are compared with those obtained by computer simulation.

A fast Fourier transform algorithm using Hadamard transform

Abstract: A fast Fourier transform (FT) algorithm using Hadamard transform (HT) is introduced, which is called HFT (Hadamard Fourier Transform). In the algorithm proposed here, a HT is used as mid-transform and the redundant calculation in the original fast FT algorithm is reduced by double transformation. The results of theoretical analysis show that the number of multiplications and additions of HFT are both decreased by 60% compared with that of traditional FFT and the executed result shows the computing speed of HFT is 1.6 to 1.7 times faster than FFT. Comparing with the similar algorithms such as WFT-II1, RFT2, it has a market improvement in computing speed and eliminates the limitatiom on the length of transform.

Efficient Implementation of Prime Factor Fourier Transforms

Abstract: The Winograd small factor Fourier transforms can be formed with a small number of common signal flow structures reminiscent of the butterfly in the Cooley Tuckey radix-2 fast Fourier transform (FFT) algorithm This paper identifies these structures and describes a versitile and compact prime factor algorithm (PFA) which incorporates them Running time and program code space requirements for this algorithm are presented and are compared to classic radix-2 and radix-4 FFT algorithms