Showing papers on "Discrete sine transform published in 2003"
TL;DR: It is hoped that this implementation and fixed-point error analysis will lead to a better understanding of the issues involved in finite register length implementation of the discrete fractional Fourier transform and will help the signal processing community make better use of the transform.
128 citations
TL;DR: This paper presents an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of Chebyshev polynomials.
Abstract: It is known that the discrete Fourier transform (DFT) used in digital signal processing can be characterized in the framework of the representation theory of algebras, namely, as the decomposition matrix for the regular module ${\mathbb{C}}[Z_n] = {\mathbb{C}}[x]/(x^n - 1)$. This characterization provides deep insight into the DFT and can be used to derive and understand the structure of its fast algorithms. In this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of Chebyshev polynomials. Then we derive most of their known algorithms by pure algebraic means. We identify the mathematical principle behind each algorithm and give insight into its structure. Our results show that the connection between algebra and digital signal processing is stronger than previously understood.
128 citations
TL;DR: The 3D discrete definition of the Radon transform is shown to be geometrically faithful as the planes used for summation exhibit no wraparound effects and there exists a special set of planes in the 3D case for which the transform is rapidly computable and invertible.
88 citations
TL;DR: A notion of ridgelet transform for arrays of digital data in which the analysis operator uses true ridge functions, as does the synthesis operator, and what is view as the key issue: the summability of the kernel underlying the constructed frame is investigated.
Abstract: We study a notion of ridgelet transform for arrays of digital data in which the analysis operator uses true ridge functions, as does the synthesis operator. There are fast algorithms for analysis, for synthesis, and for partial reconstruction. Associated with this is a transform which is a digital analog of the orthonormal ridgelet transform (but not orthonormal for finite n). In either approach, we get an overcomplete frame; the result of ridgelet transforming an n × n array is a 2n × 2n array. The analysis operator is invertible on its range; the appropriately preconditioned operator has a tightly controlled spread of singular values. There is a near-parseval relationship. Our construction exploits the recent development by Averbuch et al. (2001) of the Fast Slant Stack, a Radon transform for digital image data; it may be viewed as following a Fast Slant Stack with fast 2-d wavelet transform. A consequence of this construction is that it offers discrete objects (discrete ridgelets, discrete Radon transform, discrete Pseudopolar Fourier domain) which obey inter-relationships paralleling those in the continuum ridgelet theory (between ridgelets, Radon transform, and polar Fourier domain). We make comparisons with other notions of ridgelet transform, and we investigate what we view as the key issue: the summability of the kernel underlying the constructed frame. The sparsity observed in our current implementation is not nearly as good as the sparsity of the underlying continuum theory, so there is room for substantial progress in future implementations.
75 citations
TL;DR: A new method for the discrete fractional Fourier transform (DFRFT) computation is given and the DFRFT of any angle can be computed by a weighted summation of the D FRFTs with the special angles.
Abstract: A new method for the discrete fractional Fourier transform (DFRFT) computation is given in this paper. With the help of this method, the DFRFT of any angle can be computed by a weighted summation of the DFRFTs with the special angles.
50 citations
TL;DR: In this article, the time variant discrete Fourier transform (TVDFT) was proposed as an alternative order tracking method for rotating machinery, which is a combination of the Fast Fourier Transform (FFT) and the resampling based methods.
40 citations
01 Jan 2003
TL;DR: In this paper, a nonparametric volatility measure based on the Discrete Sine Transform (DST) is proposed, which exactly diagonalizes the covariance matrix of the MA(1) process and provides an orthonomal basis decomposition of the return process which permits to optimally disentangle the underlying ecient price signal from the time-varying nuisance component contained in tick-by-tick return series.
Abstract: Realized volatility afiords the ex-post empirical measurement of the latent notional volatility. However, the time-varying returns autocorrelation induced by microstructure efiects represents a challenging problem for standard volatility measures. In this study, a new nonparametric volatility measures based on the Discrete Sine Transform (DST) is proposed. We show that the DST exactly diagonalizes the covariance matrix of MA(1) process. This original result provides us an orthonomal basis decomposition of the return process which permits to optimally disentangle the underlying e‐cient price signal from the time-varying nuisance component contained in tick-by-tick return series. As a result, two nonparametric volatility estimators which fully exploit all the available information contained in high frequency data are constructed. Moreover the DST orthogonalization allow us to analytically compute the score and the Fischer information matrix of MA(1) processes. In discussing e‐cient numerical procedures for the likelihood maximizations we also suggest that DST estimator would represent the most valid starting point for the numerical maximization of the likelihood. Monte Carlo simulations based on a realistic model for microstructure efiects show the superiority of DST estimators, compared to alternative local volatility proxies for every level of the noise to signal ratio and a large class of noise contaminations. These properties make the DST approach a nonparametric method able to cope with time-varying autocorrelation, in a simple and e‐cient way, providing robust and accurate volatility estimates under a wide set of realistic conditions. Moreover, its computational e‐ciency makes it well suitable for real-time analysis of high frequency data.
39 citations
07 Sep 2003
TL;DR: This work addresses channel estimation based on the discrete Fourier transform (DFT) applied to OFDM-based MIMO systems and shows the proposed estimator to be optimum for the sample spaced channel, i.e. the channel tap delays are multiples of the sampling duration.
Abstract: We addresses channel estimation based on the discrete Fourier transform (DFT) applied to OFDM-based MIMO systems. By exploiting the properties of the DFT, channel estimation schemes for MIMO-OFDM system can be simplified. The Fourier transform translates phase shifts in the frequency domain to delays in the time domain. In order to exploit this feature, phase shifted pilot sequences are a perfect match to the Fourier transform in terms of separating the N/sub T/ superimposed signals, corresponding to N/sub T/ transmit antennas, without any further processing. The proposed estimator is shown to be optimum for the sample spaced channel, i.e. the channel tap delays are multiples of the sampling duration. A sub-optimum approximation for the non-sample spaced channel is also suggested.
33 citations
06 Apr 2003
TL;DR: A theorem is presented that decomposes a polynomial transform into smallerPolynomial transforms, and it is shown that the FFT is obtained as a special case, which is used to derive a new class of recursive algorithms for the discrete cosine transforms of type II and type III.
Abstract: The Cooley-Tukey FFT algorithm decomposes a discrete Fourier transform (DFT) of size n = km into smaller DFT of size k and m. In this paper we present a theorem that decomposes a polynomial transform into smaller polynomial transforms, and show that the FFT is obtained as a special case. Then we use this theorem to derive a new class of recursive algorithms for the discrete cosine transforms (DCT) of type II and type III. In contrast to other approaches, we manipulate polynomial algebras instead of transform matrix entries, which makes the derivation transparent, concise, and gives insight into the algorithms' structure. The derived algorithms have a regular structure and, for 2-power size, minimal arithmetic cost (among known DCT algorithms).
29 citations
25 May 2003
TL;DR: This work extends the Legendre transform as the slope transform to non-concave/non-convex functions and uses it to analyze a simple communication network and proposes an identification method for its transfer characteristic.
Abstract: We describe an application of the Legendre transform to communication networks. The Legendre transform applied to max-plus algebra linear systems corresponds to the Fourier transform applied to conventional linear systems. Hence, it is a powerful tool that can be applied to max-plus linear systems and their identification. Linear max-plus algebra has been already used to describe simple data communication networks. We first extend the Legendre transform as the slope transform to non-concave/non-convex functions. We then use it to analyze a simple communication network. We also propose an identification method for its transfer characteristic, and we confirm the results using the ns-2 network simulator.
28 citations
09 Nov 2003
TL;DR: This paper will propose structures for improved integer transforms in terms of improved approximation accuracy and computational efficiency, and Experimental results will show that clear improvements in these two points are achieved in lossless audio coding.
Abstract: Lifting scheme based integer transforms are very powerful tools to construct lossless coding schemes. These transforms such as the integer fast fourier transform (IntFFT) and the integer modified discrete cosine transform (IntMDCT) are integer approximations of the original floatingpoint transforms, and hence there is an approximation error in the transform domain. This paper will propose structures for improved integer transforms in terms of improved approximation accuracy and computational efficiency. Experimental results will show that clear improvements in these two points are achieved in lossless audio coding.
10 Nov 2003
TL;DR: The algorithm is based on a novel contrast measure that is defined for each DCT coefficient that can be applied to the enhancement of images compressed with JPEG and it is especially useful when it is applied to enhance the direction contrast of the images.
Abstract: In this paper a new algorithm is presented for image enhancement in the discrete cosine transform (DCT) domain. The algorithm is based on a novel contrast measure that is defined for each DCT coefficient. This algorithm can be applied to the enhancement of images compressed with JPEG and it is especially useful when it is applied to enhance the direction contrast of the images. Experimental results show the effectiveness of the proposed algorithm.
TL;DR: The careful analysis of regular structure of the new fast MDCT algorithm allows to extract a new DCT-IV/DST-IV computational structure and to suggest a new sparse matrix factorization of the D CT-IV matrix.
01 Sep 2003
TL;DR: The problem of the fast computation of the Moore–Penrose and Drazin inverse of a multi-variable polynomial matrix is addressed and the algorithms proposed, use evaluation-interpolation techniques and the Fast Fourier transform proved to be faster than other known algorithms.
Abstract: Two discrete Fourier transform based algorithms are proposed for the computation of the Moore-Penrose and Drazin inverse of a multivariable polynomial matrix.
15 Sep 2003
TL;DR: The rank-distance of primitive length (n=q/sup m/-1) linear cyclic codes over F/sub q//sup m/ is studied using the discrete Fourier transform (DFT) description of these codes.
Abstract: We study the rank-distance of primitive length (n=q/sup m/-1) linear cyclic codes over F/sub q//sup m/ using the discrete Fourier transform (DFT) description of these codes.
Patent•
22 Aug 2003TL;DR: In this article, a Fourier transform apparatus whose pipeline width is independent of transform point number of individual pipeline FFT circuits in each stage is presented, composed of a preceding stage and a succeeding stage.
Abstract: A Fourier transform apparatus whose pipeline width is independent of transform point number of individual pipeline FFT circuits in each stage and composed of a preceding stage and a succeeding stage. Each of the stages includes M(power of 2)-point radix 2 pipeline FFT circuits each having two-parallel inputs/outputs in a number of a (divisor of M) which are equal in respect to the transform point number and data permutating means for data supply to the transform means of each stage so that the pipeline width of the Fourier transform apparatus is made independent of the transform point numbers of the individual pipeline FFT circuits in each stage.
Proceedings Article•
01 Jan 2003
TL;DR: This investigation is undertaken to explore the possibilities of applying the Fourier space properties of the discrete Radon transform to the inverse problem, that of obtaining discrete projection data from continuous projection data as a means of efficient tomographic reconstruction that requires minimal interpolation and filtering.
Abstract: This paper seeks to extend the Fourier space properties of the discrete Radon transform, R(t, m), proposed by Matus and Flusser in (1), to expanded discrete projections, R(k, θ), where the wrapping of rays is removed. This expanded mode yields projections more akin to the continuous space sinogram. It is similar to the Mojette transform defined in (2), but has a pre-determined set of discrete projection angles derived from the Farey series (3). It is demonstrated that a close approx- imation to the sinogram of an image can be obtained from R(k, θ), both in Radon and Fourier space. This investigation is undertaken to explore the possibilities of applying this mapping to the inverse problem, that of obtaining discrete projection data from continuous projection data as a means of efficient tomographic reconstruction that requires minimal interpolation and filtering.
01 Jan 2003
TL;DR: It is shown that the MDCT can also be used as an analysis tool, by extracting the frequency of a pure sine wave with some simple combinations of MDCT coefficients, and studying the performance of this estimation in ideal (noiseless) conditions.
Abstract: The Modified Discrete Cosine Transform (MDCT) is a broadlyused transform for audio coding, since it allows an orthogonal time-frequency transform without blocking effects. In this article, we show that the MDCT can also be used as an analysis tool. This is illustrated by extracting the frequency of a pure sine wave with some simple combinations of MDCT coefficients. We studied the performance of this estimation in ideal (noiseless) conditions, as well as the influence of additive noise (white noise / quantization noise). This forms the basis of a low-level feature extraction directly in the compressed domain.
01 Jan 2003
TL;DR: The discrete sinusoid time-domain analysis of discrete systems, the discrete Fourier transform properties of the DFT, and the z-transform frequency- domain analysis of digital filters are studied.
Abstract: The discrete sinusoid time-domain analysis of discrete systems the discrete Fourier transform properties of the DFT the z-transform frequency-domain analysis of discrete systems digital filters - characterization and realization FIR filters IIR filters aliasing and other effects the continuous-time Fourier transform fundamentals of the PM DFT algorithms the u X 1 PM DFT algorithms DFT algorithms for real data.
TL;DR: In this paper, a discrete orthogonal Gauss-Hermite transform (DOGHT) is introduced for the analysis of optical pulse properties in the time and frequency domains.
Abstract: A discrete orthogonal Gauss–Hermite transform (DOGHT) is introduced for the analysis of optical pulse properties in the time and frequency domains. Gaussian quadrature nodes and weights are used to calculate the expansion coefficients. The discrete orthogonal properties of the DOGHT are similar to the ones satisfied by the discrete Fourier transform so the two transforms have many common characteristics. However, it is demonstrated that the DOGHT produces a more compact representation of pulses in the time and frequency domains and needs less expansion coefficients for a given accuracy. It is shown that it can be used advantageously for propagation analysis of optical signals in the linear and nonlinear regimes.
15 Oct 2003
TL;DR: In this paper, the authors proposed a new spectral estimator based on discrete cosine transform (DCT) and modified group delay function (MGD) for the clean autoregressive (AR) process.
Abstract: This paper proposes a new spectral estimator based on discrete cosine transform (DCT) and modified group delay function (MGD) (DCTMGD). The new estimator provides a significant reduction in variance and bias, better signal detection ability and frequency resolution compared with those of based on DFT (DFTMGD). The DCT provides reduced bias and hence enables good signal detection ability. The MGD enables better variance reduction without any loss in frequency resolution. For two sinusoids in noise, it has an improvement in variance of about 63% for SNR= 20 dB and 57% for SNR=0 dB, over those of DFTMGD. For the clean autoregressive (AR) process, the root mean square error (RMSE) reduces by 35% over that of DFTMGD. Further it is able to detect a sinusoid which is about 25 dB below AR spectral peaks.
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TL;DR: Construction of perfect arrays is investigated by using the Fourier transform, and a new orthogonal transform using a perfect array is discussed, which will be applied to some applications, such as communications and signal processing.
Abstract: In this paper construction of perfect arrays is investigated by using the Fourier transform, in order to discuss generally. Furthermore a new orthogonal transform using a perfect array is discussed, which will be applied to some applications, such as communications and signal processing.
Journal Article•
Patent•
14 Feb 2003
TL;DR: In this paper, a digital phase-quadrature oscillator generates a series of sine values representative of a sine wave and cosine values representing a cosine wave.
Abstract: A digital phase-quadrature oscillator generates a series of sine values representative of a sine wave, and a series of cosine values representative of a cosine wave. In each iteration of the oscillator, a sum of the squares of past sine and cosine values is used as a negative feedback term in synthesizing next sine and cosine values, in order to stabilize the amplitudes of the sine and cosine values.
Patent•
06 Aug 2003
TL;DR: In this paper, a Discrete Fourier Transform watermark is embedded into selected frequency bands of the computed magnitude domain of the DFT, thereby creating a watermarked magnitude domain.
Abstract: A Discrete Fourier Transform watermark for use with digital images/video. A Y component of a Y, U(Cb), V(Cr) digital data stream representing color components of digital video is extracted as the digital data for embedding the watermark. The digital data is then scaled to a standard size. A Discrete Fourier Transform (DFT) is performed on the digital data, and a magnitude domain of the Discrete Fourier Transform is computed. The watermark is embedded into selected frequency bands of the computed magnitude domain of the Discrete Fourier Transform, thereby creating a watermarked magnitude domain. The selected frequency bands comprise one or more middle frequency bands, and the middle frequency bands comprise a band of circular rings of the magnitude domain. An inverse Discrete Fourier Transform is performed on the watermarked magnitude domain to reconstruct the digital data with the embedded watermark.
18 Sep 2003
TL;DR: A tree-structured Haar transform for denoising stepwise signals is combined with the idea of averaging estimates from overlapping windows, and a possibility of selecting either of two different transforms for each sliding window is explored.
Abstract: Signal denoising is one of the essential areas of Haar transform application due to its wavelet-like structure and low computing requirements. Recently the Haar transform has been generalized to the case of arbitrary time and scale splitting, thereby providing an opportunity of adapting the basis functions to the signal on hand, and, at the same time, being computationally as efficient as the classical Haar transform. In this paper, an application of such a transform, called the tree-structured Haar transform, for denoising stepwise signals is combined with the idea of averaging estimates from overlapping windows. For other type of signals a possibility of selecting either of two different transforms for each sliding window-the tree-structured Haar transform and the discrete cosine transform-is explored.
Patent•
26 Jun 2003TL;DR: In this paper, a hierarchical distance calculator calculates a distance between two vectors hierarchically, starting with a vector component having a high significance, i.e., a component having large discrete and unique value in the aforementioned transforms, or a low frequency component.
Abstract: In a similarity vector detection device (2), a registration vector g and an input vector f are subjected to transform by order matrix, discrete cosine transform, discrete Fourier transform, Walsh-Hadamard transform or Karhunen-Loeve transform by vector converters (20, 21). A hierarchical distance calculator (23) calculates a distance between two vectors hierarchically, starting with a vector component having a high significance, i.e., a component having a large discrete and unique value in the aforementioned transforms, or a low frequency component. When it is judged that the accumulated value of distances calculated up to a certain hierarchy exceeds a threshold value S of the distance in the threshold value judgment section (24), the distance calculation is terminated only by outputting the fact that the threshold value S is exceeded.
06 Jul 2003
TL;DR: The intMDCT is suitable for both lossless and lossy audio coding, and inherits most of the attractive properties of the MDCT, including a good spectral representation of the audio signal, critical sampling and overlapping of blocks.
Abstract: In this paper, an efficient implementation of the forward and inverse MDCT is proposed for even-length MDCT. The algorithm uses discrete cosine transform of type II (DCT-II) to compute the forward MDCT and their inverse DCT-III to compute the inverse MDCT. The lifting scheme is used to approximate multiplications appearing in the MDCT lattice structure where the dynamic range of the lifting coefficients can be controlled by proper choices of the lifting factorizations. The new structure requires less multiplications and additions than previous reported algorithms. The new transform has the properties that it is an integer-to-integer mapping and is reversible. Moreover, it inherits most of the attractive properties of the MDCT, including a good spectral representation of the audio signal, critical sampling and overlapping of blocks. Hence, the intMDCT is suitable for both lossless and lossy audio coding.
TL;DR: In this paper, the authors bring overview of discrete Bessel representations and highlight their differences and similarities with both the discrete Fourier transform (DFT) methods and the finite basis/discrete variable representations (FBR/DVRs).
Abstract: The object of this note is to bring overview of discrete Bessel representations and to highlight their differences and similarities with both the discrete Fourier transform (DFT) methods and the finite basis/discrete variable representations (FBR/DVRs). Notably, the unpublished work of Corey and Le Roy deserves special attention. Also, the work of Littlejohn and Cargo is shown to yield an interesting derivation.
24 Nov 2003
TL;DR: A fast implementation of the 3D ridgelet transform based on discrete analytical 3D lines: the DART, which uses the Fourier strategy for the computation of the associated discrete Radon transform.
Abstract: In this paper, we present a fast implementation of the 3D ridgelet transform based on discrete analytical 3D lines: the 3D discrete analytical ridgelet transform (DART). This transform uses the Fourier strategy (the projection-slice formula) for the computation of the associated discrete Radon transform. The innovative step of the DART is the construction of 3D discrete analytical lines in the Fourier domain, that allows a fast perfect backprojection. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a DART adapted to a specific application. A denoising application is presented.