Showing papers on "Split-radix FFT algorithm published in 1978"
TL;DR: In this article, the authors show how discrete Fourier transformation can be implemented as a filter bank in a way which reduces the number of filter coefficients, leading to new forms of FFT's, among which is a \cos/sin FFT for a real signal which only employs real coefficients.
Abstract: The paper shows how discrete Fourier transformation can be implemented as a filter bank in a way which reduces the number of filter coefficients. A particular implementation of such a filter bank is directly related to the normal complex FFT algorithm. The principle developed further leads to types of DFT filter banks which utilize a minimum of complex coefficients. These implementations lead to new forms of FFT's, among which is a \cos/\sin FFT for a real signal which only employs real coefficients. The new FFT algorithms use only half as many real multiplications as does the classical FFT.
112 citations
TL;DR: This correspondence shows that if Haralick had made use of the fact that the FFT's of real sequences can be computed more rapidly than general FFTs, the result would have been reversed.
Abstract: Haralick has shown that the discrete cosine transform of N points can be computed more rapidly by taking two N-point fast Fourier transforms (FFT's) than by taking one 2N-point FFT as Ahmed had proposed. In this correspondence, we show that if Haralick had made use of the fact that the FFT's of real sequences can be computed more rapidly than general FFT's, the result would have been reversed. A modified algorithm is also presented.
77 citations
TL;DR: The performance of each of the unitary transforms in the trigonometric family is studied in terms of quantitative performance measures such as variance distribution, rate distortion, Wiener filtering and how well a transform decorrelates the data efficiently for possible bandwidth compression of a signal represented by a firstorder Markov process model.
Abstract: The feasibility of discrete sine transform (DST) and discrete sine cosine transform (DSCT) for digital image processing problems are investigated. Discrete sine transform and discrete cosine transform can be computed by using two FFT’s of original data sequence of length N. Discrete sine cosine coefficients are computed by FFT of data sequence of length N while the inverse is obtained by computing two FFT's. The performance of each of the unitary transforms in the trigonometric family is studied in terms of quantitative performance measures such as variance distribution, rate distortion, Wiener filtering and how well a transform decorrelates the data efficiently for possible bandwidth compression of a signal represented by a firstorder Markov process model. Computer simulation results on a monochrome image are presented.
74 citations
TL;DR: If the fast Fourier transfmm algorithm with n inputs, n as a power of two, is implemented with S temporary locations where S=o(n/ \log n) , then the computation time T grows faster than n\log n.
Abstract: The performance of the fast Fourier transfmm algorithm is examined under limitations on computational space and time. It is shown that if the algorithm with n inputs, n as a power of two, is implemented with S temporary locations where S=o(n/ \log n) , then the computation time T grows faster than n \log n . Furthermore, T can grow as fast as n^{2} if S=S_{min} + O(1) where S_{min}=l+\log_{2}n , the minimum necessary. These results are obtained by deriving tight bounds on T versus S and n .
60 citations
TL;DR: A high-speed, low-power, fast Fourier transform (FFT) processor that performs a 128-point FFT in 250 μs at 16-MHz clock rate and therefore can be used for applications such as frequency-division multiplexing/timedivisionmultiplexing (FDM/TDM) transmultiplexer.
Abstract: A high-speed, low-power, fast Fourier transform (FFT) processor is described in this paper. The FFT processor is designed around parallel arithmetic functions (16 by 16 multiplier and 16-bit adders) and can operate up to a 17.0-MHz clock rate. It performs a 128-point FFT in 250 μs at 16-MHz clock rate and therefore can be used for applications such as frequency-division multiplexing/timedivision multiplexing (FDM/TDM) transmultiplexer. The processor was designed and tested according to the design specifications. Its standalone feature permits its use in a variety of systems employing spectral analysis. The high-speed requirements are met by a real-time address generation scheme. The design can be used for a higher order FFT by providing extra memory space.
56 citations
TL;DR: A radix-3 FFT which has no multiplications in the three-point DFT's is introduced and the application to fast convolution of real sequences is discussed.
Abstract: A radix-3 FFT which has no multiplications in the three-point DFT's is introduced. It uses arithmetic with numbers of the form a + bμ, where μ is a complex cube root of unity. The application to fast convolution of real sequences is discussed.
55 citations
TL;DR: In this paper, a pseudo-spectral Fast Fourier Transform (FFT) is used to approximate the departure from smooth periodicity of the dependent variable distribution at each time level.
43 citations
TL;DR: The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fouriers transform (FFT).
Abstract: The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winogzad (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
29 citations
TL;DR: A calculational scheme is given for generating fluctuations which have any specified power spectrum and the fast computer-based algorithm makes use of a random number generator and fast Fourier transform routine.
Abstract: A calculational scheme is given for generating fluctuations which have any specified power spectrum. The fast computer-based algorithm makes use of a random number generator and fast Fourier transform (FFT) routine.
18 citations
TL;DR: The design for a convolution processor is presented, which employs a single highly parallel implementation of the fast Fourier transform (FFT) algorithm, eminently suited for real-time matched filtering of coded signals encountered in sonar systems.
Abstract: The design for a convolution processor is presented, which employs a single highly parallel implementation of the fast Fourier transform (FFT) algorithm. This processor is eminently suited for real-time matched filtering of coded signals encountered in sonar systems. Computer simulations have shown that this processor, which uses fixed point arithmetic and modest word sizes, can efficiently handle signals with multiple targets and relatively large Doppler shifts. The parallel architecture provides a throughput rate sufficient for computing both forward and inverse transforms in the one processor. The system is flexible permitting frequency domain adaptive beam-forming, attractive in many sonar applications.
10 citations
TL;DR: An algorithm which computes the Fourier transform of a sequence of length n over GF(2m) using approximately 2nm multiplications and n2+ nm additions is developed, which can be used when n is not highly composite or is a prime.
Abstract: An algorithm which computes the Fourier transform of a sequence of length n over GF(2m) using approximately 2nm multiplications and n2+ nm additions is developed. The number of multiplications is thus considerably smaller than the n2multiplications required for a direct evaluation, though the number of additions is slightly larger. Unlike the fast Fourier transform, this method does not depend on the factors of n and can be used when n is not highly composite or is a prime.
TL;DR: For certain large transform lengths, Winograd's algorithm for computing the discrete Fourier transform (d.f.t.) is extended considerably by performing the cyclic convolution, required by Winog Rad's method, by a fast transform over certain complex integer fields developed previously by the authors.
Abstract: For certain large transform lengths, Winograd's algorithm for computing the discrete Fourier transform (d.f.t.) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields developed previously by the authors. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (f.f.t.) or Winograd's more conventional algorithm.
IBM1
TL;DR: It is shown that for small word lengths and/or moderate to large transform lengths NTT filtering achieves a better SNR than FFT filtering with fixed-point arithmetic.
Abstract: Number Theoretic Transforms (NTT's), unlike the Discrete Fourier Transform (DFT), are defined in finite rings and fields rather than in the field of complex numbers. Some NTT's have a transform structure like the Fast Fourier Transform (FFT) and can be used for fast digital signal processing. The computational effort and the signal-to-noise ratio (SNR) performance of linear filtering in finite rings and fields are investigated. In particular, the effect of limited word lengths, i.e., b \leq 16 , and long transform lengths on the SNR is analyzed. It is shown that for small word lengths and/or moderate to large transform lengths NTT filtering achieves a better SNR than FFT filtering with fixed-point arithmetic. Some new NTT's with a single- or mixed-radix fast transform structure are presented. While these NTT's may require special modulo arithmetic they achieve optimum transform length for any given word length b in the range 8 \leq b \leq 16 .
01 Apr 1978
TL;DR: The concept of the zoom FFT (a more efficient algorithm which allows zooming in on a narrow segment of the spectrum while preserving its frequency content) is extended to the two-dimensional case and is further expanded to allow zooms over a specified segment within both the time and the frequency domains.
Abstract: The concept of the zoom FFT (a more efficient algorithm which allows zooming in on a narrow segment of the spectrum while preserving its frequency content) is extended to the two-dimensional case. The technique is further expanded to allow zooms over a specified segment within both the time and the frequency domains. Comparisons are also made as to the computational efficiency of this technique compared to the conventional two-dimensional FFT algorithms.