Showing papers on "Prime-factor FFT algorithm published in 1995"

A recursive fast Fourier transformation algorithm

Abstract: A new composite filter-bank structure is presented for the efficient implementation of the recursive discrete transformation. This structure is based on a proper combination of the concepts of polyphase filtering and the fast Fourier transformation (FFT) algorithm. Its computational complexity is in direct correspondence with the FFT, and can be operated both in sliding and block-oriented modes. The inherent parallelism of this structure enables very high speed in practical implementations. >

High-performance FFT algorithms for the Convex C4/XA supercomputer

Abstract: Some implementations of a power-of-two one-dimensional fast Fourier transform (FFT) on vector computers use radix-4 Stockham autosort kernels with a separate transpose step. This paper describes an algorithm that performs well on a Convex C4/XA vector supercomputer on large FFTs by using higher-radix kernels and moving the transpose step into the computational steps. For short transforms a different algorithm is used that calculates the FFT without storing any intermediate results to memory. Performance results using these techniques are given.

Fast Fourier transform, iteration, and least-squares-fit demodulation image processing for analysis of single-carrier fringe pattern

Abstract: Fast Fourier transform (FFT), iteration, and least-squares fit are combined to form an image-processing system for the analysis of a carrier-coded fringe pattern. Only one coded fringe pattern is needed for extracting unambiguous information. The coded fringe pattern is first two-dimensionally FFT filtered to produce an initial coded phase with the carrier phase in it. Several phase iterations are carried out if necessary to improve the coded phase. The least-squares-fit technique is used to obtain a pure carrier phase. Then the carrier is removed by subtracting the pure carrier phase from the coded phase. The algorithm offers an improvement over the Fourier-transform method reported in the literature. A program is designed to execute the algorithm, and the processing is automated by a personal computer with an image board. Theory and applications of speckle interferometry and three-dimensional contouring are presented.

New FFT bit-reversal algorithm

Abstract: Presents a very short, simple, easy to understand bit-reversal algorithm for radix-2 fast Fourier transform (FFT), which is, furthermore, easily extendable to radix-M. In addition, when implemented together with Yong's (see IEEE Trans. Acoust., Speech, Signal Processing, vol.39, no.1O, p.2365-7, 1991) technique, the computing time is comparable to that of the fastest algorithms. >

Order of N complexity transform domain adaptive filters

Abstract: Implementation of the transform domain adaptive filters is addressed. Recent results have shown that if the input data to a radix-2 fast Fourier transform (FFT) structure is sliding one sample at a time, only N-1 butterflies need to be calculated for updating the FFT structure. This is opposed to most of the previous reports that assume order of NlogN complexity for such implementation. In this correspondence, a generalization of the sliding FFT, which introduces a wide class of orthogonal transforms that can be implemented with the order of N complexity is proposed. >

Computations of multiwavelet transforms

Abstract: The pyramid algorithm for computing single wavelet transform coefficients is well-known. The pyramid algorithm can be implemented by using tree-structured multirate filter banks. In this paper, we propose a general algorithm to compute multiwavelet transform coefficients, by adding proper pre multirate filter banks before the vector filter banks that generate multiwavelets. The proposed algorithm can be though of as a discrete vector-valued wavelet transform for certain discrete-time vector-valued signals. The proposed algorithm can be also though of as a discrete multiwavelet transform for discrete-time signals. We then present some numerical experiments to illustrate the performance of the algorithm, which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms.

Algorithm 749: fast discrete cosine transform

Abstract: An in-place algorithm for the fast, direct computation of the forward and inverse discrete cosine transform is presented and evaluated. The transform length may be an arbitrary power of two.

Parallel FFT algorithms using radix 4 butterfly computation on an eight-neighbor processor array

Abstract: Fast Fourier transform (FFT), which has wide and variety application areas, requires very high speed computation. Since parallel processing of FFT is very attractive for high speed FFT computation, many processor arrays and multiprocessor systems have been proposed with efficient FFT algorithms. As a result of the recent development of VLSI technology, several massively parallel computers have been implemented on commercial basis. The MasPar, which is one of the SIMD type massively parallel computers, consists of an eight-neighbor processor array. This paper discusses parallel 1-D FFT algorithms on an eight-neighbor processor array. We propose three algorithms according to various data allocation methods. Then we estimate and evaluate their processing time. With the number of processors N = N r × N r , processing time is estimated to be 2( N r − 2) t c + ( log 2 N r ) t b , where t c is the communication time between neighbor processors, and t b is the execution time for the radix 4 butterfly computation. We also compare these algorithms with the conventional radix 2 FFT algorithm implemented on a mesh processor array. It is shown that the radix 4 FFT algorithms are faster than the radix 2 algorithms. These algorithms get high speed FFT computation by combining the radix 4 FFT algorithm with the characteristics of the eight-neighbor processor array.

Computing the inverse DFT with the in-place, in-order prime factor FFT algorithm

Abstract: We present a method for computing the inverse discrete Fourier transform (IDFT) by the in-place, in-order prime factor FFT algorithm (PFA). This is achieved by modifying the input and the output index mapping equations. This approach does not result in any additional cost in terms of program length and computational time. >

Speech coding system which uses MPEG/audio layer III encoding algorithm

Abstract: A speech coding system is shown, which comprises a linear transform unit 50 for executing linear transform on an input signal Si with a predetermined block length Sb and an FFT unit 10, 30 for executing Fast Fourier transform on the input signal Si with two different, i.e., large and small, block lengths, a block length setting unit 20 for calculating a predetermined block length Sb to be set in the linear transform unit 50 according to an FFT signal generated in the FFT unit 10, 30 and setting this block length in the linear transform unit 50, and a coding unit 80 for coding an intermediate signal Sm generated in the linear transform unit 50 to form and output a bit stream So. The FFT unit has a function of selecting a block length used for the Fast Fourier transform among two, i.e., large and small, block lengths according to a continuous portion of the input signal Si.

A FFT based algorithm for the formation of wide-angle ISAR images using EIP

Abstract: This paper describes a new algorithm for implementing wide angle imaging. The new algorithm is derived from the enhanced image processing (EIP) algorithm described by Ausherman et al. (1984) and is based on using the Fast Fourier Transform (FFT) to rotate and interpolate the linear images before compositing. The new algorithm is more accurate than the linear interpolation based compositing scheme used by Ausherman and is designed to perform efficiently on modern vector array processors. First, correlation imaging and the relationship between linear imaging and wide angle imaging is discussed. Following the discussion of the enhanced imaging technique, the new algorithm for implementing the EIP is described. After the theory is discussed, an example demonstrating the efficacy of the new algorithm is presented. The effect of different strategies for reducing sidelobes in the EIP imagery is also discussed. A comparison of the computational complexity of the new algorithm with the traditional algorithm is presented. The paper concludes with a summary.

Efficient stabilization methods for fast polynomial tranforms

Abstract: The computation of discrete polynomial transforms is a fundamental operation in the applied mathematical sciences. Much effort has been placed on the development of fast polynomial transforms, particularly those based on the fast Fourier transform. Two exact fast transform models of particular importance are the polynomial division tree model and the three-term recurrence rule model. Recent work has introduced some new fast polynomial transforms based on the two models. These algorithms have complexity at most $O(N \log\sp2 N)$, as compared to the $O(N\sp2$) direct methods; however, in some cases they display numerical instability on reasonable inputs. This thesis presents some heuristics which greatly improve the numerical reliability without sacrificing efficiency in either the asymptotic or execution time sense. For the fast transforms based on polynomial division, a heuristic technique called symmetry stabilization greatly improves the numerical reliability for the case where the sample points are on the unit circle. This technique improves the numerical reliability for three sample point distributions which arise in important applications with little or no increase in the complexity. New fast transforms based on the polynomial division model are described for generalized Chebyshev polynomials, which may also benefit from the symmetry stabilization technique. This new transform unifies the fast Fourier transform and the fast cosine transform as a single algorithm parameterized by a variable $\rho\ \in$ (0, 1). For the fast transforms based on three-term recurrence relations, a modified algorithm is described which uses stability bypass operations to improve the numerical reliability. This method has been tested extensively for transforms onto sets of associated Legendre functions, or fast Legendre transforms. The fast Legendre transform is used to effect a fast spherical harmonic transform on the 2-sphere, thereby giving an $O(N \log\sp2 N$) algorithm for convolving two functions on the sphere. Some efficient variations of the algorithm are described which are based on a "semi-naive" approach. Finally, a leveled hypercube parallel algorithm for the fast Legendre transform is described which is work optimal, and when used in conjunction with well-known parallel FFT algorithms, effects a work-optimal parallel algorithm for fast spherical harmonic transforms.

Precise expression relating the Fourier transform of a continuous signal to the fast Fourier transform of signal samples

Abstract: The fast Fourier transform (FFT) signature of a finite duration, constant frequency, time signal displays sidebands which are a sampling artifact. An analytical expression is derived which precisely predicts artifact behavior. Using this expression, a precise spectral estimate (PSE) is derived. It is demonstrated that this method outperforms the FFT with and without Hamming weighting both in estimating the magnitudes and phases of the spectral components of a time series. Furthermore, PSE is capable of resolving frequency to a fraction of an FFT frequency resolution cell.

FFT on reconfigurable hardware

Abstract: The fast Fourier transform algorithm is specified in a data parallel version of 'C'. This specification is used to produce a custom circuit suitable for use in a system based on reconfigurable logic. Performance estimates indicate that this approach is capable of producing the 2D Fourier transform of images at real time video rates.

An efficient algorithm for high resolution, power quality measurements of sparsely distributed power system harmonics and inter harmonics

Abstract: Power quality issues often are related to the presence of harmonic and nonharmonic frequencies. The authors have developed a more efficient and accurate solution than traditional FFT (fast Fourier transform) approaches. The approach combines the strengths of the FFT, CZT (chirp Z transform), and DFT (discrete Fourier transform) in a composite algorithm called the "variable search method".

Fast discrete Fourier transform with exponentially spaced points

Abstract: The use of fast algorithms for evaluation of discrete Fourier transform-inverse transform pairs with uniformly spaced input data but with output data required only at exponentially spaced intervals is investigated. The algorithms require order (N) arithmetic operations, rather than the order (N log(N)) required for the full FFT algorithm.

An optimized mass storage FFT for vector computers

Abstract: The performance of a segmented FFT algorithm which allows the out-of-core computation of the Fourier transform of a very large mass storage data array is presented. The code is particularly optimized for vector computers. Tests performed mainly on a CONVEX C210 vector computer showed that, for very long transforms, tuning of the main parameters involved leads to computation speed and global efficiency better than for FFTs performed in-core. The use of tunable parameters allows optimization of the algorithm on machines with different configurations.

A novel derivation of the Agarwal-Cooley fast cyclic convolution algorithm based on the Good-Thomas Prime Factor algorithm

Abstract: The Agarwal-Cooley fast cyclic convolution algorithm and the Good-Thomas Prime Factor algorithm have been traditionally independently derived. In this work we show how the Prime Factor Algorithm triggers the Agarwal-Cooley decomposition in the discrete time domain. A new polynomial expression based on the tensor product formulation of the Prime Factor Algorithm is used in conjunction with the cyclic convolution theorem, to obtain a novel and insightful derivation of the Agarwal-Cooley fast cyclic convolution algorithm.

A M-D FFT algorithm for symmetric signals

Abstract: Symmetric signals are defined by subsets of their support which depend on the specific symmetry. Depending on the symmetry, the cardinality of these subsets may be much smaller than that of the supports. The DFT of the symmetric signals enjoys symmetries related to the input symmetry, by which the DFT is defined by subsets the same as those defining the input signal. In principle, the computation of the DFT of symmetric signal can only use the input subset sufficient for defining the signal. In practice, all known MD FFT algorithms can only take advantage of even and odd parity's symmetries, and cannot exploit general signal symmetries for reducing the computation. This work presents a new MD FFT algorithm capable of saving computation in front of general signal's symmetries.

A fast discrete Fourier transform with unequally-spaced frequencies

Abstract: Realization of the discrete Fourier transform (DFT) as the fast Fourier transform (FFT) has a widespread application in practice There are, however, such problems in technology where the application of the FFT method does not justify satisfactory results Such problems comprise eg the analysis of short sections of fast decaying vibrations or the analysis of instantaneous values of nonstationary signal parameters Solving the problems arising in this type of signals analysis has contributed to development of the algorithm of the DFT fast computing for transient vibrations The developed method enables one to obtain high resolution for low frequencies by increasing the density of sampling of the analyzed signal The algorithm in terms of the computer program (Lenort (1989)) has been tested both on the model data and on the real signal records

Algorithm-based fault detection in prime factor FFT networks

Abstract: A concurrent error detection (CED) scheme has been proposed by Jou and Abraham (1988)for a radix-2 FFT network. The method uses a coding scheme to ensure that all the modelled faults are detectable. The same method has been applied to the prime factor algorithm (PFA) FFT network. The results show that the CED scheme is applicable to multi-factor PFA networks and it is efficient, only, for large N. Since the PFA is a minimum multiplication algorithm, it is logical to adopt a minimum multiplication CED scheme. For this purpose, a suitable CED scheme has been developed such that the data coding is no longer needed which results in less hardware and time overheads. The new scheme provides a stage-by-stage error detection without causing time delay and additional roundoff noise. The hardware overhead is substantially reduced with improved error detection performance since the scheme needs to consider the roundoff error of only one stage instead of the entire FFT network.

Pipeline optimizations of the prime factor algorithm

Abstract: The prime factor algorithm (PFA) is an efficient discrete Fourier transform (DFT) computation algorithm used when the sequence length can be decomposed into mutually prime factors. Following our previous results on PFA decomposition carried out at Caltech on hypercube machines, we present in the paper a pipeline PFA implementation suitable for multiprocessor systems with distributed memory. This implementation achieves high values of efficiency and speed-up when processing multiple sequences of data. The paper shows how an optimized structure can be obtained when the concurrency among computation and communications is exploited at each node of the pipe. Experimental results obtained on transputer-based structures and on the Intel Touchstone Delta system are also reported.

Efficient computation of the 2-D discrete pseudo-Wigner distribution by the fast Hartley transform

Abstract: Wigner distribution (WD) is useful in analyzing and processing nonstationary signals. In this paper the fast Hartley transform (FHT) approach for computing the one-dimensional discrete pseudo-Wigner distribution (1D DPWD) is extended to compute the two-dimensional (2-D) DPWD and a new fast algorithm is presented for computing the 2-D DPWD by the 2-D FHT entirely in the real domain. First, the original 2-D real signal is converted into its complex analytic version. A fast algorithm is proposed to compute the 2-D discrete Hilbert transform using the 2-D FHT instead of the 2-D complex FFT with a reduced number of real operations. Then, the algorithm formulae are derived for computing the 2-D DPWD of the analytic signal by the 2-D FHT. Compared with the conventional FFT approach, the proposed algorithm is performed entirely in the real domain, and the computational complexity is greatly reduced from 3 2-D complex FFT's to 3 2-D real FHT's.