Showing papers on "Split-radix FFT algorithm published in 1989"
TL;DR: In this article, the split-radix algorithm for the discrete Fourier transform (DFT) of length 2/sup m/ is considered, and it is shown that whenever a radix-p/p/sup 2/ outperforms a single-Radix algorithm, then a Radix-P/P/Sup 2/2/ algorithm will outperform both of them.
Abstract: The split-radix algorithm for the discrete Fourier transform (DFT) of length-2/sup m/ is considered. First, the reason why the split-radix algorithm is better than any single-radix algorithm on length-2/sup m/ DFTs is given. Then, the split-radix approach is generalized to length-p/sup m/ DFTs. It is shown that whenever a radix-p/sup 2/ outperforms a radix-p algorithm, then a radix-p/p/sup 2/ algorithm will outperform both of them. As an example, a radix-3/9 algorithm is developed for length-3/sup m/ DFTs. >
57 citations
TL;DR: The described method opens a way to compute intracerebral source localizations of ongoing EEG activity by constructing a sine-cosine diagram of the Fourier-transformed data, which is the least error compromise landscape of all possible landscapes during the paradigmatic cycle of the given FFT frequency.
Abstract: The described method opens a way to compute intracerebral source localizations of ongoing EEG activity. A sine-cosine diagram of the Fourier-transformed data is constructed for each frequency point, forming a "FFT constellation" of entries. Into the FFT constellation of each diagram, a straight line is fitted which produces the least squared deviation sum between the original entry positions and their orthogonal projections onto that line. The map landscape described by the voltages between the projected positions ("FFT approximation") is the least error compromise landscape of all possible landscapes during the paradigmatic cycle of the given FFT frequency. The map thus constructed can be used in the usual dipole source localization procedures. There is one for each FFT frequency point. The squared forward solution of the fitted dipole source and the squared FFT approximation map are "power maps" which are very similar to the original power map. For an average-reference power map with two peaks, the source tends to lie between the peaks; a power map with one peak might show closely neighboring maximal and minimal potential values in the FFT approximation, indicative of a tangential source close to the surface.
55 citations
TL;DR: A new algorithm for the fast computation of the discrete Fourier transform (DFT) is introduced, called the conjugate pair FFT (CPFFT), which is used to compute a length-2m DFT.
Abstract: A new algorithm for the fast computation of the discrete Fourier transform is introduced. The algorithm, called the conjugate pair FFT (CPFFT), is used to compute a length-2m DFT. The number of multiplications and additions required by the CPFFT is less than that required by the SRFFT algorithm.
31 citations
TL;DR: A structure theorem is devised to construct systematically various vector-radix decimation-in-frequency FFT algorithms from their 1-D counterparts.
Abstract: A general form of the matrix representation for multidimensional, vector-radix, fast Fourier transform (FFT) algorithms using decimation-in-frequency is presented. A structure theorem is devised to construct systematically various vector-radix decimation-in-frequency FFT algorithms from their 1-D counterparts. Logic diagrams are provided to facilitate the software and hardware implementation of the algorithms. The computational complexity of several of the algorithms is considered. >
28 citations
TL;DR: The author states that generally, the vector split-radix method provides a significant reduction in the number of complex multiplications required to implement a two-dimensional discrete Fourier transform.
Abstract: The complete equations are presented for the first stage of the two-dimensional vector split-radix decimation-in-frequency fast Fourier transform algorithm using a structural approach. The computational complexity of the algorithm is discussed and compared to other published results. The author states that generally, the vector split-radix method provides a significant reduction in the number of complex multiplications required to implement a two-dimensional discrete Fourier transform. >
18 citations
01 May 1989
TL;DR: This paper shows how a rectangular array of N CORDIC (co-ordinate digital computer) processing elements can be used to carry out an efficient two-dimensional systolic implementation of the N-point DFT, offering highly attractive throughput rates in relation to other N-processor solutions.
Abstract: A number of systolic architectures have appeared over the past few years for performing the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms, using both linear and orthogonal processing networks. The paper shows how a rectangular array of N CORDIC (co-ordinate digital computer) processing elements can be used to carry out an efficient two-dimensional systolic implementation of the N-point DFT, offering highly attractive throughput rates in relation to other N-processor solutions, such as the conventional linear systolic array. >
16 citations
IBM1
TL;DR: In this article, a multi-dimensional discrete Fourier series method has been developed to calculate the coupling capacitances in VLSI circuits, which is related to the known electric potential distributions by Laplace equation.
Abstract: A multi-dimensional discrete Fourier series method has been developed to calculate the coupling capacitances in VLSI circuits. In the present method a scalar potential Φ( r ) is generated, in discrete Fourier series form, which is related to the known electric potential distributions by Laplace equation. By using the multiple radix Fast Fourier Transform (FFT) algorithm to reduce the CPU time, the electric field strength can be obtained from the gradient of the scalar potential. The calculated 2-D and 3-D results generally compare well with the conventional approach results. A program has been developed and numerical results are discussed.
16 citations
TL;DR: Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured.
Abstract: The Fast Fourier Transform is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional SIMD parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Our FFT programs are compared to the currently best Cray-2 FFT library program, CFFT2.
15 citations
08 May 1989
TL;DR: In this paper, a new interpolation scheme that allows the frequency and amplitude of a sinusoid to be estimated with high accuracy is proposed. But the method is based on the fact that spectral convolution introduces spectral leakage that can be observed at the output of an FFT.
Abstract: The problem with using the FFT to do spectral estimation is that only a sampled version of the discrete Fourier transform of the input signal is provided To do parameter estimation on a signal with frequency that does not appear at the output of the FFT, one has to perform spectral interpolation to approximate the original continuous spectrum The author introduces a new interpolation scheme that allows the frequency and amplitude of a sinusoid to be estimated with high accuracy The method is based on the fact that spectral convolution introduces spectral leakage that can be observed at the output of an FFT With the minimum four-sample Blackman-Harris window, this method yields better results than the conventional parabola-fitting technique The largest error occurs when the frequency is halfway between two frequency bins Higher-order Taylor series could be used to improve the estimation in the range of 045 >
13 citations
TL;DR: In this article, the authors derived a duality equation relating the extension functions introduced in the extended function FFT (EF-FFT) method to conventional window functions and showed that signals with high-frequency content only within the observation window are best analyzed with EF-FFT methods and signals with time-distributed spectral components (e.g., speech) are best analysed with conventional FFT methods.
Abstract: The periodicity assumption implicit in fast Fourier transform (FFT) techniques can be utilized through time-domain prealiasing to obtain the spectral components of infinite-duration time-domain reflectometry signals when they can be modeled, outside the observation window, with step and/or exponential functions. The technique is shown to be more accurate than both conventional windowing and the other FFT approaches described in the literature for analysis of steplike signals. The duality equation relating the extension functions introduced in the extended function FFT (EF-FFT) method to conventional window functions is derived. Using this relation, it is shown that signals with high-frequency content only within the observation window are best analyzed with EF-FFT methods and that signals with time-distributed spectral components (e.g., speech) are best analyzed with conventional FFT methods. >
11 citations
TL;DR: In this article, it is shown that the fast Fourier transform (FFT) combines naturally with Simpson's rule for Sommerfeld-type integral computation, and several examples are provided to illustrate the process.
Abstract: It is shown that the fast Fourier transform (FFT) combines naturally with Simpson's rule for Sommerfeld-type integral computation. The principal advantage of using the FFT is that a single subroutine call yields a set of sample values of an integral (i.e. the integral for various values of an integrand parameter). Such samples could be useful in themselves. In other applications Sommerfeld integrals represent Green's functions nested within other spatial integrals, so samples from the FFT might be useful in approximating the outernested integral. Several examples are provided to illustrate the process. >
21 Aug 1989
TL;DR: This paper reports an explanation of an intricate algorithm in the terms of a potentially mechanisable rigorous-development method, using notations and techniques of Sheeran and Bird and Meertens and claiming that these techniques are applicable to digital signal processing circuits.
Abstract: This paper reports an explanation of an intricate algorithm in the terms of a potentially mechanisable rigorous-development method. It uses notations and techniques of Sheeran [1] and Bird and Meertens [2, 3]. We have claimed that these techniques are applicable to digital signal processing circuits, and have previously applied them to regular array circuits [4, 5, 6].
TL;DR: Two multiplicative FFT algorithms have operational counts close to the Winograd algorithm, but they have a better structure, which simplifies their implementation and are suited for conventional serial machines.
TL;DR: An efficient algorithm for computing the discrete cosine transform (DCT) is presented, based on an index mapping which converts an odd-length DCT to a realvalued DFT of the same length using permutations and sign changes only.
Abstract: In this letter, an efficient algorithm for computing the discrete cosine transform (DCT) is presented. It is based on an index mapping which converts an odd-length DCT to a realvalued DFT of the same length using permutations and sign changes only. The real-valued DFT can then be computed by efficient real-valued FFT algorithms such as the prime factor algorithm. The algorithm is more efficient than an earlier one because no postmultiplications are required.
23 May 1989
TL;DR: The authors describe the implementation of real and complex FFT (fast Fourier transform) algorithms on the Motorola DSP96002, a general-purpose, dual-bus IEEE standard floating-point digital signal processor that provides the basis for efficient implementation of FFTs and other fast transforms.
Abstract: The authors describe the implementation of real and complex FFT (fast Fourier transform) algorithms on the Motorola DSP96002. The DSP96002 is a general-purpose, dual-bus IEEE standard floating-point digital signal processor (DSP). At a 74-ns instruction cycle, the DSP96002 implements a 1024-point real FFT in 0.905 ms and a 1024-point complex FFT in 1.55 ms. This performance is achieved by calculating up to three floating-point results in a single instruction cycle, or 40.5 MFLOPS peak. A radix-2 FFT butterfly is executed every four cycles, an average of 33.75 IEEE MFLOPS. The instruction set and architecture of the DSP96002 provide the basis for efficient implementation of FFTs and other fast transforms, such as the discrete Walsh-Hadamard transform, discrete cosine transform, and discrete Hartley transform. >
01 Jan 1989
TL;DR: The main idea is to use the additive structure of the indexing set Z/N to define mappings of the input and output data vectors into 2-dimensional arrays which, when combined with these mappings, compute the N-point FFT.
Abstract: In the following two chapters, we will concentrate on algorithms for computing FFT of size a composite number N. The main idea is to use the additive structure of the indexing set Z/N to define mappings of the input and output data vectors into 2-dimensional arrays. Algorithms are then designed, transforming 2-dimensional arrays which, when combined with these mappings, compute the N-point FFT. The stride permutations of chapter 2 play a major role.
TL;DR: A new fast algorithm for computing the two-dimensional discrete Fourier transform DFT(2n; 2) using the fast discrete cosine transform algorithm that uses only real multiplications, which is more suitable for real input data.
Abstract: We present a new fast algorithm for computing the two-dimensional discrete Fourier transform DFT(2n; 2) using the fast discrete cosine transform algorithm. The algorithm has a lower number of multiplications and additions compared with other published algorithms for computing the two-dimensional DFT. Because it uses only real multiplications, the algorithm is more suitable for real input data.
01 Jan 1989
TL;DR: This chapter reviews fast Fouriertransform methods, a collective term for a number of efficient algorithms developed to compute the discrete Fourier transform (DFT) and the inverse discrete Fouriers transform (IDFT).
Abstract: This chapter reviews fast Fourier transform methods. The fast Fourier transform (FFT) is a collective term for a number of efficient algorithms developed to compute the discrete Fourier transform (DFT) and the inverse discrete Fourier transform (IDFT). It is not a transform in its own right, and the understanding and interpretation of FFT methods depend fundamentally on the theory and properties of the DFT. It is not difficult to run DFT programs on a microcomputer, and FFT algorithms can be quite satisfactorily demonstrated without excessive demands on memory or processing rates. Although a sound understanding of the principles and properties of the DFT is necessary to apply the FFT and interpret the output of FFT programs, in many applications, an FFT subroutine can be used as a black box without a detailed knowledge of the algorithm employed. FFT algorithms can be used to great advantage in a wide range of signal-processing applications. These include Fourier analysis and synthesis of signals and spectrum analysis in general. FFT methods can be used to implement FIR digital filters.
23 May 1989
TL;DR: A parallel adder configuration that is much faster than the usual serial adder is proposed and a scheme for fast reordering of the input data that increases the reordering speed without increasing the memory size is also proposed.
Abstract: A fast implementation of recursive DFTs (discrete Fourier transforms) is presented. It only needs (N-1)/2 real multiplications to compute all N frequency components. A factor R/sub T/ is introduced. If the ratio T/sub m//T/sub a/ of the multiplier and adder periods is greater than R/sub T/, this scheme is faster than the FFT (fast Fourier transform). The error and signal-to-noise ratio are studied. A parallel adder configuration that is much faster than the usual serial adder is proposed. A scheme for fast reordering of the input data that increases the reordering speed without increasing the memory size is also proposed. >
26 Jun 1989
TL;DR: A spectrum analyzer is presented for three-phase inverter-fed balanced machine systems that is capable of calculating up to 24 harmonic components of the line currents every 130 mu s.
Abstract: A spectrum analyzer for three-phase inverter-fed balanced systems which is capable of calculating up to 24 harmonic components of the line currents every 130 mu s is presented. The method is based on a synchronized sampling technique and on a highly efficient fast Fourier transform (FFT) for three-phase systems. The latter consists of a two-dimensional six-point discrete Fourier transform (DFT) followed by a two-dimensional four-point DFT. The total FFT algorithm has been successfully implemented on a TMS32010 digital signal processor. >
03 Jan 1989
TL;DR: One of the Fast Fourier Transform algorithms, the Prime Factor algorithm (PFA), is implemented on the hypercube using a concurrent communication algorithm, called the Crystal_Router, to overcome the extra communication requirement up to a certain number of processors.
Abstract: We have implemented one of the Fast Fourier Transform algorithms, the Prime Factor algorithm (PFA), on the hypercube. On sequential computers, the PFA and other discrete Fourier transforms (DFT) such as the Winograd algorithm (WFA) are known to be very efficient. However, both algorithms require full data shuffling and are thus challenging to any distributed memory parallel computers. We use a concurrent communication algorithm, called the Crystal_Router for communicating shuffled data. We will show that the speed gained in reduced arithmetic compared to binary FFT is sufficient to overcome the extra communication requirement up to a certain number of processors. Beyond this point the standard Cooley-Tukey FFT algorithm has the best performance. We comment briefly on the application of the DFT to signal processing in synthetic aperture radar (SAR).
23 May 1989
TL;DR: It is shown that if r/sub 1/=r/sub 2//sup k/ a radix-r/ sub 1/ FFT can be easily put in a digit-reversed order based on radix r/ sub 2/.
Abstract: Implementation of the FFT (fast Fourier transform) on currently available DSP (digital signal processing) devices is facilitated by hardware bit-reverse counters that are used for the unscrambling of the data. C.S. Burrus (1988) showed how these counters can also be used in the case of higher radix algorithms. The concept is generalized here to radices r/sub 1/ and r/sub 2/. It is shown that if r/sub 1/=r/sub 2//sup k/ a radix-r/sub 1/ FFT can be easily put in a digit-reversed order based on radix r/sub 2/. For instance, a radix-4 or radix-8 FFT can be put in a bit-reversed (i.e. radix-2) order without any extra computation or data movement. >
TL;DR: An efficient operation applied prior to fast Fourier transform (FFT) processing is described that enables one to obtain the same spectral resolution with shorter FFTs.
Abstract: An efficient operation applied prior to fast Fourier transform (FFT) processing is described that enables one to obtain the same spectral resolution with shorter FFTs. This so-called prefolding operation is complementary to zero fill. Both techniques are described. >
TL;DR: An algorithm is presented for the computation of large size fast Fourier transforms for computer-generated holograms when the recording device has a very large space-bandwidth product and the computation is under memory restrictions.
Abstract: An algorithm is presented for the computation of large size fast Fourier transforms (FFTs) for computer-generated holograms. The algorithm is useful when the recording device has a very large space-bandwidth product and the computation is under memory restrictions. The number of complex operations required using this algorithm is slightly larger than the number of operations necessary using the FFT algorithm.
TL;DR: This paper presents a two dimensional FFT program (SW2DFFT), a Fortran program capable of handling large data matrices both square and rectangular, based on the decomposed Cooley-Tukey algorithm.
TL;DR: A fast algorithm for the arbitrary polynomial transformation is described, based on the fast Fourier transform algorithm, which reduces the computational complexity of a recently proposed recursive algorithm by an order of magnitude.
Abstract: A fast algorithm for the arbitrary polynomial transformation is described. This algorithm is based on the fast Fourier transform (FFT) algorithm and reduces the computational complexity of a recently proposed recursive algorithm by an order of magnitude. >
TL;DR: Criteria are established for choosing the best way to formulate and implement a conjugate gradient FFT (fast Fourier transform) method.
Abstract: Criteria are established for choosing the best way to formulate and implement a conjugate gradient FFT (fast Fourier transform) method. Also, the issues of speed and convergence are addressed in co...
26 Mar 1989
TL;DR: A multi-radix fast Fourier number theoretic transform is proposed for the calculation of the discrete Fourier transform of sequences with a prime length P=2/sup k1/*3/ Sup k2/*5/Sup k3/+1, where k1, k2, and k3 are integers.
Abstract: A multi-radix fast Fourier number theoretic transform is proposed for the calculation of the discrete Fourier transform of sequences with a prime length P=2/sup k1/*3/sup k2/*5/sup k3/+1, where k1, k2, and k3 are integers. Advantages include availability of fast algorithms for a set of prime lengths, residue arithmetic with benefit in speed and hardware cost, and parallel implementation. A discrete power spectrum example is included. >
01 Jan 1989
TL;DR: The authors present a method to efficiently implement the recursive instrumental variable (RIV) algorithm, which is often encountered in many practical applications, and its fast Fourier transform (FFT) implementation is discussed.
Abstract: The authors present a method to efficiently implement the recursive instrumental variable (RIV) algorithm, which is often encountered in many practical applications. A sequential block-processing algorithm is derived, and its fast Fourier transform (FFT) implementation is discussed. Under several easily met conditions, this method can offer a remarkable computational advantage over the previous fast-RIV. To accommodate the slowly time-varying input situations, an exponentially windowed extension of the result is also given. >
TL;DR: An efficient algorithm for performing a fast Fourier transform on a data parallel computer is presented that allows both the decimation in time and Danielson–Lanczos phases to be executed in log(N) steps, where N is the size of the transform.
Abstract: An efficient algorithm for performing a fast Fourier transform on a data parallel computer is presented. The algorithm allows both the decimation in time (bit reversal) and Danielson–Lanczos (butterfly) phases to be executed in log(N) steps, where N is the size of the transform. Pseudocode is given for implementing the algorithm on a Connection Machine.