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Showing papers on "Discrete sine transform published in 1974"


Journal ArticleDOI
TL;DR: In this article, a discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed, which can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering.
Abstract: A discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed. It is shown that the discrete cosine transform can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering. Its performance is compared with that of a class of orthogonal transforms and is found to compare closely to that of the Karhunen-Loeve transform, which is known to be optimal. The performances of the Karhunen-Loeve and discrete cosine transforms are also found to compare closely with respect to the rate-distortion criterion.

4,481 citations


Journal ArticleDOI
TL;DR: The CORDIC iteration is applied to several Fourier transform algorithms and a new, especially attractive FFT computer architecture is presented as an example of the utility of this technique.
Abstract: The CORDIC iteration is applied to several Fourier transform algorithms. The number of operations is found as a function of transform method and radix representation. Using these representations, several hardware configurations are examined for cost, speed, and complexity tradeoffs. A new, especially attractive FFT computer architecture is presented as an example of the utility of this technique. Compensated and modified CORDIC algorithms are also developed.

304 citations


Journal ArticleDOI
TL;DR: The discrete Fourier transform is applied as a coarse estimator of the frequency of a sine wave in Gaussian noise to estimate signal energy-to-noise density ratio E/N_0.
Abstract: The discrete Fourier transform (DFT) is applied as a coarse estimator of the frequency of a sine wave in Gaussian noise. Probability of anomaly and the variance of the estimation error are determined by computer simulation for several DFT block sizes as a function of signal energy-to-noise density ratio \mathcal{E}/N_0 . Several data windows are considered, but uniform weighting gives the best performance.

86 citations


Patent
20 Aug 1974
TL;DR: In this article, two parallel shift registers store and shift the real and imaginary components of the complex number X k + iY k, successively shifted one bit per strobe in response to receipt of new data.
Abstract: A wholly digital system for computing the discrete Fourier transform of sequentially received data in a recursive fashion. Two parallel shift registers store and shift the real and imaginary components of the complex number X k + iY k . The data in the parallel registers are successively shifted one bit per strobe in response to receipt of new data. Additional logic operates recursively on successive data inputs to compute the discrete Fourier transform.

33 citations


Journal ArticleDOI
01 Jan 1974
TL;DR: A new discrete linear transform for image compression which is used in conjunction with differential pulse-code modulation on spatially adjacent transformed subimage samples and finds that for low compression rates, the Karhunen-Loeve outperforms both the Hadamard and the discrete linear basis method.
Abstract: Transform image data compression consists of dividing the image into a number of nonoverlapping subimage regions and quantizing and coding the transform of the data from each subimage. Karhunen-Loeve, Hadamard, and Fourier transforms are most commonly used in transform image compression. This paper presents a new discrete linear transform for image compression which we use in conjunction with differential pulse-code modulation on spatially adjacent transformed subimage samples. For a set of thirty-three 64 × 64 images of eleven different categories, we compare the performancea of the discrete linear transform compression technique with the Karhunen-Loeve and Hadamard transform techniques. Our measure of performance is the mean-squared error between the original image and the reconstructed image. We multiply the mean-squared error with a factor indicating the degree to which the error is spatially correlated. We find that for low compression rates, the Karhunen-Loeve outperforms both the Hadamard and the discrete linear basis method. However, for high compression rates, the performance of the discrete transform method is very close to that of the Karhunen-Loeve transform. The discrete linear transform method performs much better than the Hadamard transform method for all compression rates.

25 citations


Book ChapterDOI
01 Oct 1974

17 citations


Journal ArticleDOI
TL;DR: In this paper, a class of generalized continuous transforms for the orthogonal decomposition of signals is presented, governed by a definition of time translation in terms of signed-bit dyadic time shift.
Abstract: This paper presents a class of generalized continuous transforms for the orthogonal decomposition of signals. Base functions for the continuous transform range from Walsh functions of order two to stair-like functions which resemble approximations to sinusoids and which are distinct from the generalized Walsh functions. Standard desirable properties which are shown to hold for the generalized continuous transform operator include orthogonality of the base functions, linearity of the transform operator, inverse transformability, and admissibility to fast transform representation. The transform class is governed by a definition of time translation in terms of signed-bit dyadic time shift. Mathematical properties leading to this definition are discussed and the impact of the definition is assessed. Properties of the continuous class of generalized transforms make feasible analysis which could be extremely tedious using matrix representations of the operations actually mechanized in a sampled-data system. Analysis techniques are illustrated with a target detection system which is conceptually designed using the generalized continuous transform and implemented using fast transform algorithms to perform correlation operations. Since the correlation operations are valid for inputs which include signals represented in terms of Walsh functions, the example illustrates one instance in which the binary Fourier representation (BIFORE) transform can be used for practical pattern recognition.

10 citations


Journal ArticleDOI
TL;DR: In this paper, the analysis of rounding error in the one-dimensional fast Fourier transform (FFT) is extended to a class of generalized orthogonal transforms with a common fast algorithm similar to the FFT algorithm.
Abstract: The analysis of rounding error in the one-dimensional fast Fourier transform (FFT) is extended to a class of generalized orthogonal transforms [1] with a common fast algorithm similar to the FFT algorithm. This class includes the BInary FOurier REpresentation (BIFORE) transform (BT) [2], the complex BT (CBT) [3], and the discrete Fourier transform (DFT). Expressions for the mean square error (MSE) in the two-dimensional BT, CBT, and FFT are derived. In the case of white input data, the mean square error-to-signal ratio is derived for the multidimensional generalized transforms. The error-to-signal ratio for the one-dimensional FFT derived by Kaneko and Liu is modified with improvement. Some comparisons among BIFORE, DFT, and Haar transforms are also included. The theoretical results for the two-dimensional FFT and BIFORE have been verified experimentally. The experimental results are in good agreement with the theoretical results for lower order sequences, but deviate as the order increases due to the actual manner of rounding in the digital computer.

8 citations


Journal ArticleDOI
Simon Haykin1
01 Jul 1974
TL;DR: In this article, a unified survey and treatment of the different forms of the Hilbert transform which arise in the study of digital signal processing systems when considering: (a) the frequency-domain relations between the real and imaginary components of the network function of a linear stable digital filter whose impulse response is causal, and (b) the determination of analytic signals associated with periodic waveforms or sequences specified in the time domain.
Abstract: The paper presents two aspects of the Hilbert transform; first, a unified survey and treatment of the different forms of the Hilbert transform which arise in the study of digital signal processing systems when considering: (a) the frequency-domain relations between the real and imaginary components of the network function of a linear stable digital filter whose impulse response is causal, and (b) the determination of analytic signals associated with periodic waveforms or sequences specified in the time domain. The continuous forms of the Hilbert transform are developed as special cases of the corresponding discrete cases. Secondly, a comparison of two finiteimpulse response (f.i.r.) digital filters for realising the discrete Hilbert transform is made.

5 citations


Journal ArticleDOI
R. Diderich1
01 Oct 1974
TL;DR: A previous technique for deriving Chebyshev shading coefficients using a cosine series is rewritten in the form of an inverse discrete Fourier transform (DFT) thus allowing one to take advantage of standard DFT algorithms.
Abstract: A previous technique for deriving Chebyshev shading coefficients using a cosine series is rewritten in the form of an inverse discrete Fourier transform (DFT) thus allowing one to take advantage of standard DFT algorithms. The reduced accuracy required for intermediate calculations is retained. Additionally, the fast Fourier transform can be used giving computational savings.

2 citations



Journal ArticleDOI
TL;DR: A matrix method which computes discrete Fourier transforms using a digital computer program which takes advantage of symmetry of the complex functions about the real and imaginary axes to reduce the number of calculations necessary in a given Fourier transform.