Showing papers on "Discrete sine transform published in 2004"

Algorithms for Spectral Analysis of Irregularly Sampled Time Series

Abstract: In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.

Nonlinear Microwave Circuit Design

Abstract: Preface.Chapter 1. Nonlinear Analysis Methods.1.1 Introduction.1.2 Time-Domain Solution.1.3 Solution Through Series Expansion1.4 The Conversion Matrix.1.5 Bibliography.Chapter 2. Nonlinear Measurements.2.1 Introduction.2.2 Load/Source-Pull.2.3 The Vector Nonlinear Network Analyser.2.4 Pulsed Measurements.2.5 Bibliography.Chapter 3. Nonlinear Models.3.1 Introduction.3.2 Physical Models.3.3 Equivalent-Circuit Models.3.4 Black-Box Models.3.5 Simplified Models.3.6 Bibliography.Chapter 4. Power Amplifiers.4.1 Introduction.4.2 Classes of Operation.4.3 Simplified Class-A Fundamental-Frequency Design For High Efficiency.4.4 Multi-Harmonic Design For High Power And Efficiency.4.5 Bibliography.Chapter 5. Oscillators.5.1 Introduction.5.2 Linear Stability and Oscillation Conditions.5.3 From Linear To Nonlinear: Quasi-Large-Signal Oscillation And Stability Conditions.5.4 Design Methods.5.5 Nonlinear Analysis Methods For Oscillators.5.6 Noise.5.7 Bibliography.Chapter 6. Frequency Multipliers and Dividers.6.1 Introduction.6.2 Passive Multipliers.6.3 Active Multipliers.6.4 Frequency Dividers-The Rigenerative (Passive) Approach.6.5 Bibliography.Chapter 7. Mixers. 7.1 Introduction.7.2 Mixer Configurations.7.3 Mixer Design.7.4 Nonlinear Analysis.7.5 Noise.7.6 Bibliography.Chapter 8. Stability and Injection-locked Circuits.8.1 Introduction.8.2 Local Stability Of Nonlinear Circuits In Large-Signal Regime.8.3 Nonlinear Analysis, Stability And Bifurcations.8.4 Injection Locking.8.5 Bibliography.Appendix.A.1. Transformation in the Fourier Domain of the Linear Differential Equation.A.2. Time-Frequency Transformations.A.3 Generalized Fourier Transformation for the Volterra Series Expansion.A.4 Discrete Fourier Transform and Inverse Discrete Fourier Transform for Periodic Signals.A.5 The Harmonic Balance System of Equations for the Example Circuit with N=3.A.6 The Jacobian MatrixA.7 Multi-dimensional Discrete Fourier Transform and Inverse Discrete Fourier Transform for quasi-periodic signals.A.8 Oversampled Discrete Fourier Transform and Inverse Discrete Fourier Transform for Quasi-Periodic Signals.A.9 Derivation of Simplified Transport Equations.A.10 Determination of the Stability of a Linear Network.A.11 Determination of the Locking Range of an Injection-Locked Oscillator.Index.

Fast algorithms for the computation of sliding discrete sinusoidal transforms

Abstract: Fast algorithms for computing various discrete cosine transforms and discrete sine transforms in a sliding window are proposed. The algorithms are based on a recursive relationship between three subsequent local transform spectra. Efficient inverse algorithms for signal processing in a sliding window are also presented. The computational complexity of the algorithms is compared with that of known fast discrete sinusoidal transforms and running recursive algorithms.

Dilating Gabor transform for the fringe analysis of 3-D shape measurement

Abstract: In order to overcome the limitations of conventional Fourier transform and Gabor transform analyzing nonstationary signals, dilating Gabor transform is applied to analyze the optical fringes of 3-D shape measurement. The dilating Gabor transformation is introduced by using a changeable window of Gaussian function in a conventional Gabor transform. This phase analysis method provides more accurate results than Fourier transform and Gabor transform. Simulation and experimental results are presented that demonstrate the validity of the principle.

Reversible transform for lossy and lossless 2-D data compression

Abstract: A 2D transform and its inverse have an implementation as a sequence of lifting steps arranged for reduced computational complexity (i.e., reducing a number of non-trivial operations). This transform pair has energy compaction properties similar to the discrete cosine transform (DCT), and is also lossless and scale-free. As compared to a separable DCT transform implemented as 1D DCT transforms applied separably to rows and columns of a 2D data block, the transforms operations are re-arranged into a cascade of elementary transforms, including the 2×2 Hadamard transform, and 2×2 transforms incorporating lifting rotations. These elementary transforms have implementations as a sequence of lifting operations.

Identification and location of hot spots in proteins using the short-time discrete Fourier transform

Abstract: A new approach for the identification and location of hot spots in proteins based on the short-time discrete Fourier transform (DFT) is proposed. In the new approach the short-time DFT of the protein numerical sequence is first computed and its columns are then multiplied by the DFT coefficients. By performing this step, the hot spot locations can be clearly identified by distinct peaks in the spectrum, thus achieving good localization in the amino acid domain.

Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

Abstract: A versatile method is described for the practical computation of the exact discrete Fourier transforms (DFT), both the direct and the inverse ones, of a continuous function g given by its values gj at the points of a uniform grid FN generated by conjugacy classes of elements of finite adjoint order N in the fundamental region F of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when F is reduced to a one-dimensional segment, and for SU(2)×SU(2)×⋯×SU(2) in multidimensional cases. This simplest case turns out to be a version of the discrete cosine transform (DCT). Implementations, abbreviated as DGT for Discrete Group Transform, based on simple Lie groups of higher ranks, are to be considered separately. DCT is often taken to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of the two inverse discrete transforms are studied. The following properties of the continuous extension of DCT (called CEDCT) from the discrete tj∈FN to all t∈F are proven and exemplified. Like the standard DFT, the DCT also returns the exact values of {gj} on the N+1 points of the grid. However, unlike the continuous extension of the standard DFT: (a) The CEDCT function fN(t) closely approximates g(t) between the points of the grid as well; (b) for increasing N, the derivative of fN(t) converges to the derivative of g(t); (c) for CEDCT the principle of locality is valid. In this article we also use the continuous extension of the two-dimensional (2D) DCT, SU(2)×SU(2), to illustrate its potential for interpolation as well as for the data compression of 2D images.

Generalized eigenvectors and fractionalization of offset DFTs and DCTs

Abstract: The offset discrete Fourier transform (DFT) is a discrete transform with kernel exp[-j2/spl pi/(m-a)(n-b)/N]. It is more generalized and flexible than the original DFT and has very close relations with the discrete cosine transform (DCT) of type 4 (DCT-IV), DCT-VIII, discrete sine transform (DST)-IV, DST-VIII, and discrete Hartley transform (DHT)-IV. In this paper, we derive the eigenvectors/eigenvalues of the offset DFT, especially for the case where a+b is an integer. By convolution theorem, we can derive the close form eigenvector sets of the offset DFT when a+b is an integer. We also show the general form of the eigenvectors in this case. Then, we use the eigenvectors/eigenvalues of the offset DFT to derive the eigenvectors/eigenvalues of the DCT-IV, DCT-VIII, DST-IV, DST-VIII, and DHT-IV. After the eigenvectors/eigenvalues are derived, we can use the eigenvectors-decomposition method to derive the fractional operations of the offset DFT, DCT-IV, DCT-VIII, DST-IV, DST-VIII, and DHT-IV. These fractional operations are more flexible than the original ones and can be used for filter design, data compression, encryption, and watermarking, etc.

A new transform for 2-D signal representation (MRT) and some of its properties

Abstract: A new transform (MRT) for two-dimensional signal representation and some of its properties are proposed in this paper. The transform helps to do the frequency domain analysis of two-dimensional signals without any complex operations but in terms of real additions. It is obtained by exploiting the periodicity and symmetry of the exponential term in the discrete Fourier transform (DFT) relation, and by grouping related data. Forward and inverse relations of the transform are presented. The transform coefficients show useful redundancies among themselves. These redundancies, which can be used to implement the transform, are studied. A few properties of the transform are studied and the relevant relations are presented.

Comments on Hilbert Transform Based Signal Analysis

Abstract: The use of the Hilbert transform for time/frequency analysis of signals is briefly considered. While the Hilbert transform is based on arbitrary continuous signals, most practical signals are digitially sampled and time-limited. To avoid aliasing in the sampling process the signals must also be bandlimited. It is argued that it is reasonable to consider such sampled signals as periodic (this is the basis of the Discrete Fourier Transform [DFT]) since any other interpretation is inconsistent. A simple derivation of the Hilbert transform for a sampled, periodic is then given. It is shown that the instantaneous frequency can be easily computed from the Discrete Fourier Series (or, equivalently, the DFT) representation of the signal. Since this representation is exact, the Hilbert transform representation is also exact.

Efficient recursive structures for forward and inverse discrete cosine transform

Abstract: In this paper, efficient architectures for realizing the recursive discrete cosine transform (DCT) and the recursive inverse DCT (IDCT) are proposed. By respectively folding the inputs of the DCT and the outputs of the IDCT, efficient formulations of the DCT and IDCT are derived to construct the transform kernels. The data throughput per transformation is twice that of the existing methods by spending only half of the computational cycles used by the single folding algorithms. To further improve efficiency, the double folding recursive architectures of the DCT and IDCT are developed. The computational cycles of the DCT are half of the single folding method, and the data throughput of the IDCT is twice that of the single folding method. The regular and modular properties of the proposed recursive architectures are suitable for very large scale integration (VLSI) implementation. With high throughput advantage, the proposed structures could be implemented with less power consumption, which could be applied to low rate video in mobile and portable information appliances.

Fourier fringe processing by use of an interpolated Fourier-transform technique

Abstract: Recently a powerful Fourier transform technique was introduced that was able to extract the phase from only one image. However, because the method is based on the two-dimensional Fourier transform, it inherently suffers from leakage effects. A novel procedure is proposed that does not exhibit this distortion. The procedure uses localized information and estimates both the unknown frequencies and the phases of the fringe pattern (using an interpolated fast Fourier transform method). This allows us to demodulate the fringe pattern without any distortion. The proposed technique is validated on both computer simulations and the profile measurements of a tube.

A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

Abstract: A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

Signal-processing apparatus and method

Abstract: First and second coefficients are fed into a Fast Fourier Transform unit through real number input and imaginary number input portions thereof, respectively, to perform the Fast Fourier Transform of the entered first and second coefficients, thereby producing a frequency-domain coefficient vector. The Fast Fourier Transform of an input signal is performed to transform the input signal into a frequency-domain signal vector. Thereafter, the transformed signal vector is multiplied by the coefficient vector for each element, thereby providing a multiplication result. The Inverse Fast Fourier Transform of the multiplication result renders real number output and imaginary number output portions of the inverse transformation result as first and second series of output signals, respectively.

Fast, prime factor, discrete Fourier transform

Abstract: In this paper it is shown that Winograds algorithm for computing convolutions and a fast, prime factor, discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2 m

Iterative approximation environments for modeling the evolution of an image propagating through a physical medium in restoration and other applications

Abstract: Image processing utilizing numerical calculation of fractional exponential powers of a diagonalizable numerical transform operator for use in an iterative or other larger computational environments. In one implementation, a computation involving a similarity transformation is partitioned so that one part remains fixed and may be reused in subsequent iterations. The numerical transform operator may be a discrete Fourier transform operator, discrete fractional Fourier transform operator, centered discrete fractional Fourier transform operator, and other operators, modeling propagation through physical media. Such iterative environments for these types of numerical calculations are useful in correcting the focus of misfocused images which may originate from optical processes involving light (for example, with a lens or lens system) or from particle beams (for example, in electron microscopy or ion lithography).

The centered discrete fractional Fourier transform and linear chirp signals

Abstract: The basis functions for the fractional Fourier transform are chirp signals where a precise relationship between the fractional parameter and the chirp angle can be established. The recently introduced centered discrete fractional Fourier transform, based on the Gr/spl uml/nbaum commuting matrix, has basis functions that have a sigmoidal instantaneous frequency and produces a transform that is approximately an impulse for discrete chirps. However, no such precise relation between the fractional parameter and the chirp rate of the basis functions exists in the discrete case. We study the relationship between the chirp rate and the fractional parameter in the discrete case and specifically look at two approximate expressions that relate the chirp rate and the angle for which one obtains an impulse-like transform. We study the efficacy of these estimates by applying them to the analysis of monocomponent and two component chirp signals.

Improved integer transforms using multi-dimensional lifting

Abstract: Recently lifting-based integer transforms have received much attention, especially in the area of lossless audio and image coding. The usual approach is to apply the lifting scheme to each Givens rotation. Especially in the case of long transform sizes in audio coding applications, this leads to a considerable approximation error in the frequency domain. This paper presents a multidimensional lifting approach for reducing this approximation error. In this approach, large parts of the transform are calculated without rounding operations, only the output is rounded and added. The new approach is applied and evaluated for both the Integer Modified Discrete Cosine Transform (IntMDCT) and the Integer Fast Fourier Transform (IntFFT).

Facial identification using transformed domain by SVM

Abstract: In this paper, we propose a facial biometric identification system, using transformed domains such as discrete cosine transforms (DCT), fast Fourier transforms (FFT) and discrete wavelets transforms (DWT). As novel classifier system has been utilized a support vector machines (SVM) (Burges, 1998), and in addition, the way of computing transformed coefficients. With the above system, it has been obtained a simple and robust system with good results, upper to 98% with the ORL face database (400 images) from Olivetti Research Laboratory.

Digital filter algorithm of the sine and cosine transform

Abstract: Based on the sine and cosine transform which is the special case of the Hankel transform, applying the mature theory of the fast Hankel transform, this paper derived the digital filter algorithm of the sine and cosine transform and gave 250 filter coefficients for each. An example of calculating Lipschitz integral which can be calculated by analysis, the numerical results show that this algorithm can give high precision and is suitable for spreading its use.

An optimized algorithm for computing the modified discrete cosine transform and its inverse transform

Abstract: This paper presents an optimized algorithm for the modified discrete cosine transform (MDCT) and its inverse transform (IMDCT) computation in MPEG audio. The proposed algorithm is based on the DCT of type II (DCT-II). By extracting a common kernel form from the MDCT and IMDCT, we can obtain an optimized computation of the MDCT and the IMDCT using a unified structure. Also, our proposed structure is more symmetrical and simple than those of the existing researches. Proposed algorithm is, moreover, very useful in implementing the parallel VLSI system structure of the MDCT and IMDCT.

Reality preserving fractional transforms [signal processing applications]

Abstract: The unitarity property of transforms is useful in many applications (source compression, transmission, watermarking, to name a few). In many cases, when a transform is applied on real-valued data, it is very useful to obtain real-valued coefficients (i.e. a reality-preserving transform). In most applications, the decorrelation property of the transform is of importance and it would be very useful to control it under some transform parameter (e.g. in joint source-channel coding). This paper focuses on fractional transforms, as tools for obtaining such properties. We propose a methodology for obtaining them and obtain variants of the discrete fractional cosine (sine) transform which share real-valuedness as well as most of the properties required for a fractional transform matrix. As shown in (I. Venturini et al. IEEE Trans. Signal Proc.), such matrices cannot be symmetric.

A novel algorithm for computing the 1-D discrete Hartley transform

Abstract: An efficient split algorithm for calculating the one-dimensional discrete Hartley transforms, by using a special partitioning in the frequency domain, is introduced. The partition determines a fast paired transform that splits the 2/sup r/-point unitary Hartley transform into a set of 2/sup r-n/-point odd-frequency Hartley transforms, n=1:r. A proposed method of calculation of the 2/sup r/-point Hartley transform requires 2/sup r-1/(r-3)+2 multiplications and 2/sup r-1/(r+9)-r/sup 2/-3r-6 additions.