Showing papers on "Prime-factor FFT algorithm published in 1999"
TL;DR: An algorithm to reconstruct a high- resolution image from multiple aliased low-resolution images, which is based on the generalized deconvolution technique, and it is shown that the artifact caused by inaccurate motion information is reduced by regular- ization.
Abstract: While high-resolution images are required for various applica- tions, aliased low-resolution images are only available due to the physi- cal limitations of sensors. We propose an algorithm to reconstruct a high- resolution image from multiple aliased low-resolution images, which is based on the generalized deconvolution technique. The conventional approaches are based on the discrete Fourier transform (DFT) since the aliasing effect is easily analyzed in the frequency domain. However, the useful solution may not be available in many cases, i.e., the underdeter- mined cases or the insufficient subpixel information cases. To compen- sate for such ill-posedness, the generalized regularization is adopted in the spatial domain. Furthermore, the usage of the discrete cosine trans- form (DCT) instead of the DFT leads to a computationally efficient recon- struction algorithm. The validity of the proposed algorithm is both theo- retically and experimentally demonstrated. It is also shown that the artifact caused by inaccurate motion information is reduced by regular- ization. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)00508-5)
142 citations
TL;DR: In this paper, an effective numerical algorithm based on inverting a specialized Laplace transform is derived for computing the two-dimensional power-series expansion coefficients of a two-variable function.
Abstract: An effective numerical algorithm based on inverting a specialized Laplace transform is derived for computing the two-dimensional power-series expansion coefficients of a two-variable function. Due to the special structure of the constructed 2D Laplace transform, the accuracy of the inverted function values can be assured effectively by the generalized Riemann zeta function evaluation and the multiple sets of 2D FFT computation. Therefore, the algorithm is particularly amenable to modern computers having multiprocessors and/or vector processors.
72 citations
Posted Content•
TL;DR: A new algorithm for reducing an arbitrary unitary matrix U into a sequence of elementary operations that can be used to manipulate an array of quantum bits and shows that the Fast Fourier Transform (FFT) algorithm is a special case of this algorithm.
Abstract: We present a new algorithm for reducing an arbitrary unitary matrix U into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). Our algorithm applies recursively a mathematical technique called the CS Decomposition to build a binary tree of matrices whose product, in some order, equals the original matrix U. We show that the Fast Fourier Transform (FFT) algorithm is a special case of our algorithm. We report on a C++ program called “Qubiter” that implements the ideas of this paper. Qubiter(PATENT PENDING) source code is publicly available.
44 citations
TL;DR: An efficient algorithm for computing the real-valued FFT using radix-2 decimation-in-frequency (DIF) approach has been introduced and a C++ program that implements this algorithm has been included.
Abstract: An efficient algorithm for computing the real-valued FFT (of length N) using radix-2 decimation-in-frequency (DIF) approach has been introduced. The fact that the odd coefficients are the DFT values of an N/2-length linear phase sequence introduces a redundancy in the form of the symmetry X(2k+1)=X/sup */(N-2k-1), which can be exploited to reduce the arithmetic complexity and memory requirements. The arithmetic complexity and, memory requirements of the algorithm presented are exactly the same as the most efficient decimation-in-time (DIT) algorithm for the real-valued FFT that exists to date. A C++ program that implements this algorithm has been included.
31 citations
TL;DR: This paper presents an optimized column fast Fourier transform (FFT) architecture, which utilizes bit-serial arithmetic and dynamic reconfiguration to achieve a complete overlap between computation and communication.
Abstract: This paper presents an optimized column fast Fourier transform (FFT) architecture, which utilizes bit-serial arithmetic and dynamic reconfiguration to achieve a complete overlap between computation and communication. As a result, for a clock rate of 40 MHz, the system can compute a 24-b precision 1K point complex FFT transform in 9.2 /spl mu/s, far surpassing the performance of any existing FFT systems.
28 citations
TL;DR: In this paper, a fast algorithm for electromagnetic scattering by buried conducting plates of large size and arbitrary shape using the conjugate gradient (CG) method combined with the fast Fourier transform (FFT) was presented.
Abstract: This letter presents a fast algorithm for electromagnetic scattering by buried conducting plates of large size and arbitrary shape using the conjugate gradient (CG) method combined with the fast Fourier transform (FFT). Due to the use of FFT in handling the cyclic convolutions related to Toeplitz matrices, the Sommerfeld integrals' evaluation for the buried scattering problem, which is usually time consuming, has been reduced to a minimum. The memory required for this algorithm is of the order N-the number of unknowns-and the computational complexity is of order N/sub iter/NlogN (N/sub iter/ is the iteration number N/sub iter//spl Lt/N for large problems).
27 citations
01 Aug 1999
TL;DR: The new algorithm presented in the paper has been implemented in the POLYNOMIAL Toolbox for MATLAB™, Version 2.0 and its performance highly exceeds that of older procedures used in Version 1.6.
Abstract: Fast Fourier Transform algorithm, the powerful technique of Discrete Fourier Transform, is used here to compute the determinant of a polynomial matrix. The new algorithm presented in the paper has been implemented in the POLYNOMIAL Toolbox for Matlab™, Version 2.0 and its performance highly exceeds that of older procedures used in Version 1.6. The new method is both much less costly and much more reliable and also naturally handles polynomial matrices with complex coefficients. Experimental testing results are also reported in the paper.
27 citations
TL;DR: A novel algorithm of the wavelet packets transform, which is more suitable than the multiresolution signal decomposition (MRSD) algorithm to process the practical signals in analytical instrumental analysis, was proposed and application of the methods to de-noising of noisy chromatograms was investigated.
Abstract: A novel algorithm of the wavelet packets transform, which is more suitable than the multiresolution signal decomposition (MRSD) algorithm to process the practical signals in analytical instrumental analysis, was proposed. There is no limitation of data length for the algorithm like the MRSD algorithm and, sometimes, no need to perform the inverse transform in practical uses by the algorithm. Two methods for de-noising were proposed based on the algorithm, and application of the methods to de-noising of noisy chromatograms was investigated. The results showed that the efficiency of the proposed methods is higher than that of the conventional thresholding methods.
21 citations
01 Dec 1999
TL;DR: This paper presents an efficient implementation of the pipeline FFT processor based on the radix-4 decimation-in-time algorithm with the use of digit-serial arithmetic units that can not only achieve nearly 100% hardware utilization, but also require much less memory compared with the previous digit- serial FFT processors.
Abstract: This paper presents an efficient implementation of the pipeline FFT processor based on the radix-4 decimation-in-time algorithm with the use of digit-serial arithmetic units. By splitting the sequential input sample into parallel digit-serial data streams, the proposed architecture can not only achieve nearly 100% hardware utilization, but also require much less memory compared with the previous digit-serial FFT processors. Furthermore, in FFT processors, several modules of ROM are required for the storage of twiddle factors. By exploiting the redundancy of the factors, the overall ROM size can be effectively reduced by a factor of 2.
17 citations
TL;DR: The number of multiplications necessary to compute the proposed algorithm is significantly reduced while the number of additions remains almost identical to that of conventional Multidimensional FFT's (MFFT).
Abstract: In this paper, we propose a new approach for computing multidimensional Cooley-Tukey FFT‘s that is suitable for implementation on a variety of multiprocessor architectures. Our algorithm is derived in this paper from a Cooley decimation-in-time algorithm by using an appropriate indexing process and the tensor product properties. It is proved that the number of multiplications necessary to compute our proposed algorithm is significantly reduced while the number of additions remains almost identical to that of conventional Multidimensional FFT‘s (MFFT). Comparison results show the powerful performance of the proposed MFFT algorithm against the row-column FFT transform when data dimension M is large. Furthermore, this algorithm, presented in a simple matrix form, will be much easier to implement in practice. Connections of the proposed approach with well-known DFT algorithms are included in this paper and many variations of the proposed algorithm are also pointed out.
14 citations
TL;DR: The index-reversed complex conjugate sequence and the mirror symmetric complex conjjugate sequence were defined and a significant reduction in the number of complex computations is achieved if a sequence in either domain exhibits such symmetry.
Abstract: The discrete Fourier transform (DFT) and the inverse discrete Fourier transform (IDFT) are used in a wide variety of signal processing applications. Even with the increased speed of modern processors, there is an ongoing need to further develop more efficient methods for computing DFT and IDFT, with a particular effort to reduce the number of complex multiplications. The properties of certain complex sequences are extraordinarily useful in the sense that they lead to data manipulation schemes that result in the sequences to which traditional but much shorter fast Fourier transform (FFT) algorithms may be applied. This is achieved by exploiting a certain regularity in the complex data. The index-reversed complex conjugate sequence and the mirror symmetric complex conjugate sequence were defined. A significant reduction in the number of complex computations is achieved if a sequence in either domain exhibits such symmetry.
Patent•
02 Aug 1999
TL;DR: In this paper, a transposeless 2-dimensional FFT with minimum number of clock cycles and minimum complexity is presented. But the complexity of the circuit is reduced by elimination of butterfly computation structure and adaptation of transpose-less 2D transform architecture.
Abstract: A circuit for performing Fast Fourier Transform (FFT) with minimum number of clock cycles and minimum complexity. One-dimensional FFT of size N=N 0 ×N 1 × . . . ×N M−1 , N m m=0, 1, . . . , M−1, positive numbers, is computed recursively, through a sequence of two-dimensional row-column transform computations of sizes, N 0 ×N 1 , (N 0 ×N 1 )×N 2 , (N 0 ×N 1 ×N 2 )×N 3 , . . . , (N 0 ×N 1 × . . . ×N M−2 )×N M−1 with twiddle factors. The complexity of the circuit is reduced by elimination of butterfly computation structure and adaptation of transposeless 2-D transform architecture.
Patent•
21 Jun 1999TL;DR: In this article, a parallel FFT generating system for generating a Fast Fourier Transform (FFT) of an input vector is described, which includes a plurality of processes configured to receive the input vector and process the input vectors in parallel in relation to a set of twiddle factors to generate an output vector.
Abstract: A parallel FFT generating system is disclosed for generating a Fast Fourier Transform (FFT) of an input vector. The parallel FFT generating system includes a plurality of processes configured to receive the input vector and process the input vector in parallel in relation to a set of twiddle factors to generate an output vector, the output vector comprising a Fourier transform representation of the input vector.
23 Aug 1999
TL;DR: A DRAM-like pipelined commutator architecture is used in order to reduce the required chip area for the sequential processing of 8 K complex data, and the proposed structure brings about the 55% chip size reduction compared with conventional approach.
Abstract: In this paper we propose an implementation method for a single-chip 8192 complex point FFT in terms of sequential data processing. In order to reduce the required chip area for the sequential processing of 8 K complex data, a DRAM-like pipelined commutator architecture is used. The 16-point FFT is a basic building block of the entire FFT chip, and the 8192-point FFT consists of the cascaded blocks with six stages of radix-4 and one stage of radix-2. Since each stage requires rounding of the resulting bits while maintaining the proper S/N ratio, the convergent block floating point (CBFP) algorithm is used for the effective internal bit rounding. As a result the proposed structure brings about the 55% chip size reduction compared with conventional approach.
26 Oct 1999
TL;DR: A DRAM-like pipelined commutator architecture is used to reduce the required chip area for the sequential processing of 2 K complex data, and the convergent block floating point (CBFP) algorithm is used for the effective internal bit rounding.
Abstract: In this paper, we propose an implementation method for a single-chip 2048 complex point FFT in terms of sequential data processing. In order to reduce the required chip area for the sequential processing of 2 K complex data, a DRAM-like pipelined commutator architecture is used. The 16-point FFT is a basic building block of the entire FFT chip, and the 2048-point FFT consists of the cascaded blocks with five stages of radix-4 and one stage of radix-2. Since each stage requires rounding of the resulting bits while maintaining the proper S/N ratio, the convergent block floating point (CBFP) algorithm is used for the effective internal bit rounding. As a result, the proposed structure brings about the 55% chip size reduction compared with the conventional approach.
15 Mar 1999
TL;DR: A sample-by-sample version of the block algorithm is presented and a low complexity implementation of this algorithm is developed using a similar approach to the FAP algorithm, alleviating the drawbacks of the F AP algorithm.
Abstract: The block algorithm has illustrated significant improvement in performance over the NLMS algorithm. However, it is known that block processing algorithms have lower tracking capabilities than their sample-by-sample counterparts. The fast affine projection (FAP) algorithm also outperforms the NLMS with a slight increase in complexity, but involves the fast calculation of the inverse of a covariance matrix of the input data that could undermine the performance of the algorithm. In this paper, we present a sample-by-sample version of the block algorithm and develop a low complexity implementation of this algorithm using a similar approach to the FAP algorithm. The new fast algorithm does not require matrix inversion thus alleviating the drawbacks of the FAP algorithm. A variable step size version of the proposed algorithm is also presented.
TL;DR: In this paper, a simple and general mapping procedure is proposed to minimize the computational overhead of prime factor fast algorithms for various discrete transforms, and the algorithm is shown to be computationally efficient.
Abstract: Prime factor fast algorithms are computationally efficient for various discrete transforms. However, they generally need an index mapping process to convert a one-dimensional input sequence into a two-dimensional array, which results in a substantial computational overhead and an irregular computational structure. The author attempts to minimise the computational overhead by a simple and general mapping procedure.
TL;DR: The algorithm derived in this paper is derived from a Cooley decimation-in-time algorithm by using an appropriate indexing process and it is proved that the number of multiplications necessary to compute the proposed algorithm is significantly reduced while theNumber of additions remains almost identical to that of conventional 2D FFT's.
Abstract: In this paper, we propose a new approach for computing 2D FFT's that are suitable for implementation on a systolic array architecture. Our algorithm is derived in this paper from a Cooley decimation-in-time algorithm by using an appropriate indexing process. It is proved that the number of multiplications necessary to compute our proposed algorithm is significantly reduced while the number of additions remains almost identical to that of conventional 2D FFT's. Comparison results show the good performance of the proposed 2D FFT algorithm against the row-column FFT transform. Copyright © 1999 John Wiley & Sons, Ltd.
TL;DR: In this paper, it was shown that using the Loeffler's (see Proc. IEEE ICASSP, vol.38, p.297-305, 1991) two-dimensional (2-D) 8/spl times/8-point DCT algorithm will result in an optimal algorithm in the sense of multiplicative complexity theory.
TL;DR: A multidimensional fast Fourier transform (FFT) algorithm is presented for signals with arbitrary symmetries and periodic on arbitrary lattices that makes the frequency domain computation of Volterra filtering more convenient than the time domain approach.
Abstract: A multidimensional fast Fourier transform (FFT) algorithm is presented for signals with arbitrary symmetries and periodic on arbitrary lattices. Applications that can benefit from such an algorithm include Volterra filtering and analysis of x-ray diffraction data. The presented algorithm exploits signal redundancy to achieve a computational complexity of N log N, where N is the number of independent samples. To the authors’ knowledge, this is the only FFT that makes the frequency domain computation of Volterra filtering more convenient than the time domain approach.
TL;DR: A new implementation of the two-dimensional FFT (2-D FFT) has reduced arithmetic complexity and computational savings are achieved because the 2-D case enables, after some modifications of the basic separable algorithm, scaling and inverse scaling of butterfly operators.
Abstract: A a new implementation of the two-dimensional FFT (2-D FFT) is proposed. Compared with the usual separable solution, the new realization of the 2-D FFT has reduced arithmetic complexity. Computational savings are achieved because the 2-D case enables, after some modifications of the basic separable algorithm, scaling and inverse scaling of butterfly operators. The new improvement is also applied to other 2-D transforms: DCT-IV, DCT, and lapped transforms.
Patent•
09 Jul 1999TL;DR: In this article, a system tests analog and mixed signal IC devices using an FFT algorithm, supported by a non-iterative Fast Fourier Transform (FFT) coherency analysis algorithm.
Abstract: A system tests analog and mixed signal IC devices using an FFT algorithm, supported by a non-iterative Fast Fourier Transform (FFT) coherency analysis algorithm to establish FFT sample-set coherency. A test signal is input into the IC device, and an output signal from the IC device is analyzed using the FFT algorithm. The non-iterative FFT coherency analysis algorithm uses only one “given” value and two approximated values related to a test signal. Based on these given and approximated values, the correct set of all four values required for proper testing of the IC device is determined in a single pass, without the need for multiple iterations.
TL;DR: The range-gated fast Fourier transform is the most common implementation of the optimum receiver for radar signals having random phase, frequency, and arrival time, but in practice the receiver is only optimum for input signals with frequency equal to an FFT bin frequency.
Abstract: The range-gated fast Fourier transform (FFT) is the most common implementation of the optimum receiver for radar signals having random phase, frequency, and arrival time. In practice, the receiver is only optimum for input signals with frequency equal to an FFT bin frequency. Here the discrete wavelet transform (DWT) is applied to the FFT output to recover processing gain (PG) lost for nonoptimum input signals. Since the FFT and FFT-DWT have optimum performance for different input frequencies, these algorithms can be combined by binary integration (BI) to result in a dramatically improved worst case PG over frequency.
Journal Article•
TL;DR: A new algorithm based on the discrete Fourier transform (DFT) is presented for the determination of the parameters that characterize a periodic signal and the simillation result shows the availability and superiority of the algorithm compared with existing algorithms.
Abstract: A new algorithm based on the discrete Fourier transform (DFT) is presented for the determination of the parameters that characterize a periodic signal The accuracy measurement of the signal can be achieved with a suitable windowing operation in time domain and an interpolation algorithm in frequency domain The simillation result shows the availability and superiority of the algorithm compared with existing algorithms The stability of the new method with respect to noise is verified by the noise analysis
Patent•
30 Oct 1999TL;DR: In this paper, a technique for computationally efficient evaluation of the Modified Discrete Cosine Transform (MDCT) using the Fast Fourier Transform (FFT) method is presented.
Abstract: A technique for computationally efficient evaluation of the Modified Discrete Cosine Transform (MDCT) using the Fast Fourier Transform (FFT) method is presented. The full MDCT computation process comprises of a pre-processing block, an N-Point FFT block and finally a post-processing block. It is well known that an N/2-Point FFT can be used for computing N-Point FFT of a sequence of N real data. The input to the FFT block described above consist of a sequence of N complex numbers. This patent discusses a method by which the regularity in these complex data can be exploited to compute their N-Point FFT using an N/2-Point FFT only, thereby decreasing computation burden almost by two.
27 Aug 1999
TL;DR: In this paper, the PSR far from its maximum was calculated in the case of a F/3 system working at 4000 nm, in focus and in presence of small defocusing.
Abstract: We are interested in calculating precisely the PSR far from its maximum, where the maxima of the irradiance are falling to 1E-06, or less. The first and most used method consist in calculating the Fourier transform of the wavefront using the Fast Fourier Transform algorithm (FFT). Another method is using the beam superposition technique (BST) to decompose the wavefront in Gaussian beams, propagate those beams, and recompose to obtain the result. The third method is to apply the exact equations derived at the end of last century and described in reference books like Born and Wolf or Marechel and Francon. We shall compare the result obtained with the three methods, FFT, BST, and exact calculation in the case of a F/3 system working at 4000 nm, in focus and in presence of small defocusing.
TL;DR: In this article, a fast root finding algorithm based on an FFT implementation is proposed, thus avoiding the need for a computationally heavy polynomial rooting technique that estimates the eigenvalues of a companion matrix.
Abstract: A fast root finding algorithm based on an FFT implementation is proposed, thus avoiding the need for a computationally heavy polynomial rooting technique that estimates the eigenvalues of a companion matrix. The minimum-phase polynomial factorisation proposed by Oppenheim and Schafer (1989) is first extended to an arbitrary radius factorisation, then used to extract the roots in an iterative manner.
TL;DR: This paper presents a new method of implementing the fast Fourier transform (FFT) algorithm that efficiently utilizes computer time to perform the FFT computation while data acquisition proceeds so that local butterfly modules are built using the data points that are already available.
Abstract: On-line running spectral analysis is of considerable interest in many electrophysiological signals, such as the EEG (electroencephalograph). This paper presents a new method of implementing the fast Fourier transform (FFT) algorithm. Our "real-time FFT algorithm" efficiently utilizes computer time to perform the FFT computation while data acquisition proceeds so that local butterfly modules are built using the data points that are already available. The real-time FFT algorithm is developed using the decimation-in-time split-radix FFT (DIT sr-FFT) butterfly structure. In order to demonstate the synchronization ability of the proposed algorithm, the authors develop a method of evaluating the number of arithmetic operations that it requires. Both the derivation and the experimental result show that the real-time FFT algorithm is superior to the conventional whole-block FFT algorithm in synchronizing with the data acquisition process. Given that the FFT sizeN=2 r , real-time implementation of the FFT algorithm requires only 2/r the computational time required by the whole-block FFT algorithm.
Journal Article•
TL;DR: A generalized wavelet transform multiscale Fourier transform was adopted in estimating disparities between a stereo pair, by which traditional phase based stereo matching is improved.
Abstract: A generalized wavelet transform multiscale Fourier transform was adopted in estimating disparities between a stereo pair, by which traditional phase based stereo matching is improved. It can avoid the problem that the character frequency is significantly different from the center frequency of bandpass filter and directly compute 2 D disparities and match the images without relative and absolute caliberation. The algorithm can obtain high computing efficiency by FFT. The experiments show the algorithm is practicable.
15 Mar 1999
TL;DR: This algorithm achieves a reduction of complexity with regard to the IIR-QR algorithm by using a block reduction transformation and derives a fast version of the algorithm from the rotation-based lattice algorithm (QR-LSL).
Abstract: In this paper, we present a new QR based algorithm for IIR adaptive filtering. This algorithm achieves a reduction of complexity with regard to the IIR-QR algorithm by using a block reduction transformation. Moreover, this new approach makes it possible to directly transform the fast FIR algorithm into fast O(N) versions of the IIR algorithm. Therefore, we derive a fast version of the algorithm from the rotation-based lattice algorithm (QR-LSL). Simulations, have proven the fast convergence and the good numerical properties of both algorithms for systems satisfying the strictly positive real (SPR) condition.