Showing papers on "Discrete sine transform published in 2010"

Cluster expansion and the configurational theory of alloys

Abstract: A rigorous mathematical foundation for the cluster-expansion method is presented It is shown that the cluster basis developed by Sanchez et al [Physica A 128, 334 (1984)] is a multidimensional discrete Fourier transform while the general formalism of Sanchez [Phys Rev B 48, 14013 (1993)] corresponds to a multidimensional discrete wavelet transform For functions that depend nonlinearly on the concentration, it is shown that the cluster basis corresponding to a multidimensional discrete Fourier transform does not converge, as it is usually assumed, to a finite cluster expansion or to an Ising-type model representation of the energy of formation of alloys The multidimensional wavelet transform, based on a variable basis cluster expansion, is shown to provide a satisfactory solution to the deficiencies of the discrete Fourier-transform approach Several examples aimed at illustrating the main findings and conclusions of this work are given

Accurate, Guaranteed Stable, Sliding Discrete Fourier Transform [DSP Tips & Tricks]

Abstract: This article presented a novel method of computing the SDFT that we call the modulated SDFT (mSDFT). The sliding discrete Fourier transform (SDFT) is a recursive algorithm that computes a DFT on a sample-by-sample basis. The accumulated errors and potential instabilities inherent in traditional SDFT algorithms are drastically reduced in the mSDFT. We removed the twiddle factor from the feedback in a traditional SDFT resonator and thus the finite precision of its representation is no longer a problem.

A Space-Vector Discrete Fourier Transform for Unbalanced and Distorted Three-Phase Signals

Abstract: In this paper, a space-vector discrete-time Fourier transform is proposed for fast and precise detection of the fundamental-frequency and harmonic positive- and negative-sequence vector components of three-phase input signals. The discrete Fourier transform is applied to the three-phase signals represented by Clarke's αβ vector. It is shown that the complex numbers output from the Fourier transform are the instantaneous values of the positive- and negative-sequence harmonic component vectors of the input three-phase signals. The method allows the computation of any desired positive- or negative-sequence fundamental-frequency or harmonic vector component of the input signal. A recursive algorithm for low-effort online implementation is also presented. The detection performance for variable-frequency and interharmonic input signals is discussed. The proposed and other usual method performances are compared through simulations and experiments.

Double-image encryption based on the affine transform and the gyrator transform

Abstract: We propose a kind of double-image-encryption algorithm by using the affine transform in the gyrator transform domain. Two original images are converted into the real part and the imaginary part of a complex function by employing the affine transform. And then the complex function is encoded and transformed into the gyrator domain. The affine transform, the encoding and the gyrator transform are performed twice in this encryption method. The parameters in the affine transform and the gyrator transform are regarded as the key for the encryption algorithm. Some numerical simulations have validated the feasibility of the proposed image encryption scheme.

Uniform Discrete Curvelet Transform

Abstract: An implementation of the discrete curvelet transform is proposed in this work. The transform is based on and has the same order of complexity as the Fast Fourier Transform (FFT). The discrete curvelet functions are defined by a parameterized family of smooth windowed functions that satisfies two conditions: i) 2π periodic; ii) their squares form a partition of unity. The transform is named the uniform discrete curvelet transform (UDCT) because the centers of the curvelet functions at each resolution are positioned on a uniform lattice. The forward and inverse transform form a tight and self-dual frame, in the sense that they are the exact transpose of each other. Generalization to M dimensional version of the UDCT is also presented. The novel discrete transform has several advantages over existing transforms, such as lower redundancy ratio, hierarchical data structure and ease of implementation.

A novel transform for image compression

Abstract: In this paper, we propose an orthogonal multiplication-free transform of order that is an integral power of two by an appropriate extension of the well-known fourthorder integer discrete cosine transform. Moreover, we develop an efficient algorithm for its fast computation. It is shown that the computational and structural complexities of the algorithm are similar to that of the Hadamard transform. By applying the proposed transform to image compression, we show that it outperforms the existing transforms having complexities similar to that of the proposed one.

The Discrete Fourier Transform, Part 6: Cross-Correlation

Abstract: This paper is part 6 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on correlation. The correlation is performed in the time domain (slow correlation) and in the frequency domain using a Short-Time Fourier Transform (STFT). When the Fourier transform is an FFT, the correlation is said to be a “fast” correlation. The approach requires that each time segment be transformed into the frequency domain after it is windowed. Overlapping windows temporally isolate the signal by amplitude modulation with an apodizing function. The selection of overlap parameters is done on an ad-hoc basis, as is the apodizing function selection. This report is a part of project Fenestratus, from the skunk-works of DocJava, Inc. Fenestratus comes from the Latin and means, “to furnish with windows”.

Continuous and Discrete Time Signals and Systems

Abstract: 1. Introduction to signals 2. Introduction to systems Part I. Continuous Time Signals and Systems: 3. Time domain analysis of systems 4. Signal representation using Fourier series 5. Continuous-time Fourier transform 6. Laplace transform 7. Continuous-time filters 8. Case studies for CT systems Part II. Discrete Time Signals and Systems: 9. Sampling and quantization 10. Time domain analysis 11. Discrete-time Fourier series and transform 12. Discrete Fourier transform 13. Z-transform 14. Digital filters 15. FIR filter design 16. IIR filter design 17. Applications of digital signal processing Bibliography Appendices: A. Mathematical tables B. Introduction to complex numbers C. Linear constant coefficient differential equations D. Partial fraction expansion E. Introduction to MATLAB F. About the CD-ROM.

OC-seislet: Seislet transform construction with differential offset continuation

Abstract: Many of the geophysical data-analysis problems such as signal-noise separation and data regularization are conveniently formulated in a transform domain, in which the signal appears sparse. Classic transforms such as the Fourier transform or the digital wavelet transform (DWT) fail occasionally in processing complex seismic wavefields because of the nonstationarity of seismic data in time and space dimensions. We present a sparse multiscale transform domain specifically tailored to seismic reflection data. The new wavelet-like transform — the OC-seislet transform — uses a differential offset-continuation (OC) operator that predicts prestack reflection data in offset, midpoint, and time coordinates. It provides a high compression of reflection events. Its compression properties indicate the potential of OC seislets for applications such as seismic data regularization or noise attenuation. Results of applying the method to synthetic and field data examples demonstrate that the OC-seislet transform can recon...

Research on the application of 4-weighted fractional Fourier transform in communication system

Abstract: The paper reveals the relationship between the weighting coefficients and weighted functions via the research of coefficients matrix and based on the original definition of 4-weighted fractional Fourier transform (4-WFRFT). The multi-parameters expression of weighting coefficients are given. Moreover, the 4-WFRFT of discrete sequences is defined by introducing DFT into it, which makes it suitable for digital communication systems. After analyzing the properties of WFRFT, a typical scheme for modulation/demodulation is proposed, which could make the statistics properties of the real and image part on both of the time and frequency domain and the phase properties have a significant variation. Such a variation could be controlled by the adjustment of transform parameters. If the WFRFT of multi-parameters is implemented, it will be more difficult to intercept and capture the modulated signals than normal.

Ultrafast Fourier Transform with a Femtosecond-Laser-Driven Molecule

Abstract: Wave functions of electrically neutral systems can be used as information carriers to replace real charges in the present Si-based circuit, whose further integration will result in a possible disaster where current leakage is unavoidable with insulators thinned to atomic levels We have experimentally demonstrated a new logic gate based on the temporal evolution of a wave function An optically tailored vibrational wave packet in the iodine molecule implements four- and eight-element discrete Fourier transform with arbitrary real and imaginary inputs The evolution time is 145 fs, which is shorter than the typical clock period of the current fastest Si-based computers by 3 orders of magnitudes

A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data

Abstract: A Cauchy problem for elliptic equations with nonhomogeneous Neumann datain a cylindrical domain is investigated in this paper. For the theoretical aspect the a-prioriand a-posteriori parameter choice rules are suggested and the corresponding error estimatesare obtained. About the numerical aspect, for a simple case results given by twomethods based on the discrete Sine transform and the finite difference method are presented;an idea of left-preconditioned GMRES (Generalized Minimum Residual) methodis proposed to deal with the high dimensional case to save the time; a view of dealingwith a general domain is suggested. Some ill-posed problems regularized by the quasiboundary-value method are listed and some rules of this method are suggested.

An overview of indoor OFDM/DMT optical wireless communication systems

Abstract: This paper is an overview of indoor OFDM (orthogonal frequency division multiplexing)/DMT (discrete multitone) optical wireless (OW) communication systems. Indoor OW OFDM/DMT systems can be classified into two groups. One group produces half-wave symmetry time signal at the output of the OFDM modulator by special assignment of subcarriers. Thus, allowing signal clipping at the zero level and avoiding the need of DC bias at the expense of data rate reduction. ACOOFDM (asymmetrically clipped OFDM system) and PAM (pulse amplitude modulation)-DMT are two techniques from the first group. The second group assigns data to all possible subcarriers to increase the data rate. However, half-wave symmetry signals cannot be achieved and DC bias is needed to convert the bipolar signal to a unipolar signal before modulating the LED (light emitting diode) intensity. DC-biased OFDM and a novel technique, proposed in this paper, called orthogonal PAM-DMT (OPAM-DMT) that is an extension of the proposed PAM-DMT by using discrete sine transform and discrete cosine transform to transmit two orthogonal signals at the same time, are two techniques from the second group. This paper considerers a practical LED model and studies the performance of all these systems in terms of average electrical OFDM signal power versus bit-error-ratio (BER) in the presence of additive white Gaussian noise channel (AWGN). It is shown that LED clipping has significant impact on the performance of all these systems and the performance of these systems substantially depends on the considered modulation order.

Spatial parameters for audio coding: MDCT domain analysis and synthesis

Abstract: We use Modified Discrete Cosine Transform (MDCT) to analyze and synthesize spatial parameters. MDCT in itself lacks phase information and energy conservation, which are needed by spatial parameters representation. Completing MDCT with Modified Discrete Sine Transform (MDST) into "MDCT-j*MDST" overcomes this and enables the representation in a form similar to that of DFT. And due to overlap-add in time domain, a MDST spectrum can be built perfectly from MDCT spectra of neighboring frames through matrix-vector multiplication. The matrix is heavily diagonal and keeping only a small number of its sub-diagonals is sufficient for approximation. When using MDCT based core coder in spatial audio coding, like Advanced Audio Coding (AAC), we need no separate transforming for spatial processing, cutting down significantly the computational complexity. Subjective listening tests also show that MDCT domain spatial processing has no quality impairment.

The discrete multiple-parameter fractional Fourier transform

Abstract: As a generalization of the Fourier transform (FT), the fractional Fourier transform (FRFT) has many applications in the areas of optics, signal processing, information security, etc. Therefore, the efficient discrete computational method is the vital fundament for the application of the fractional Fourier transform. The multiple-parameter fractional Fourier transform (MPFRFT) is a generalized fractional Fourier transform, which not only includes FRFT as special cases, but also provides a unified framework for the study of FRFT. In this paper, we present in detail the discretization method of the MPFRFT and define the discrete multiple-parameter fractional Fourier transform (DMPFRFT). Then, we utilize the tensor product to define two-dimensional multiple-parameter fractional Fourier transform (2D-MPFRFT) and the corresponding two-dimensional discrete multiple-parameter fractional Fourier transform (2D-DMPFRFT). Finally, as an application, a novel image encryption method based on 2D-DMPFRFT is proposed. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

Improved Coding-Theoretic and Subspace-Based Decoding Algorithms for a Wider Class of DCT and DST Codes

Abstract: The decoding of a class of discrete cosine transform (DCT) and discrete sine transform (DST) codes that are maximum distance separable codes (MDS) is considered in this paper. These class of codes are considered for error correction over real fields. All the existing algebraic decoding algorithms are capable of decoding only a subclass of these codes [which can be characterized into the Bose-Chaudhuri-Hocquenghem (BCH) form], and fails to decode the remaining even though they are MDS. In this paper, we propose a new generic algorithm along the lines of coding theoretic and subspace methods to decode the entire class of MDS DCT and DST codes. The proposed subspace approaches are similar to popular ESPRIT and MUSIC algorithms. The proposed algorithms also perform significantly better than the existing algorithms on the BCH-like subclass. A perturbation analysis is also presented to study the effect of various parameters on the error localization due to the quantization noise. Simulation results are presented to demonstrate the capability of proposed algorithms to decode the entire class and to perform significantly better on the BCH-like subclass than the existing algorithm under the influence of quantization noise.

Compensator and Compensation Method for Audio Frame Loss in Modified Discrete Cosine Transform Domain

Abstract: A compensation method for audio frame loss in a Modified Discrete Cosine Transform (MDCT) domain is provided in the present invention The method include: step a, when the frame currently lost is the p-th frame, obtaining a set of frequency points to be predicted; for each frequency point of said set, using the phases and magnitudes of the multiple frames preceding the (p-1)-th frame in the Modified Discrete Cosine Transform - Modified Discrete Sine Transform (MDCT-MDST) domain to predict the phase and magnitude of the p-th frame; using the predicted phase and magnitude to gain the MDCT coefficients corresponding to each frequency point of the p-th frame; step b, for the frequency points of a frame except for said set, using the coefficient values of the multiple frames preceding the p-th frame to calculate the MDCT coefficient values of the p-th frame at said frequency points; step c, performing an inverse MDCT on the MDCT coefficients of the p-th frame at all frequency points to gain the time domain signal of the p-th frame A compensator for the frame loss is also provided in the invention The invention has advantages of no delay, small calculation amount as well as storage amount and easy implementation

Low Complexity and Fast Computation for Recursive MDCT and IMDCT Algorithms

Abstract: Fast algorithms are derived for modified discrete cosine transform (MDCT) and inverse MDCT (IMDCT) in this brief. The proposed algorithms based on type II discrete cosine transform and type II discrete sine transform not only adopt a unified architecture for both MDCT and IMDCT computations but also take only N/8 + 1 computational cycles for each output sequence. Compared with previous IMDCT approaches, the number of preprocessing multiplications of the proposed IMDCT algorithm is reduced by 87.5%. In addition, the coefficient requirements for preprocessing in the proposed IMDCT algorithm can be reduced by 50%, and the number of multiplications for the recursive kernel is greatly decreased by up to 87.5%. The proposed algorithms in terms of hardware costs take two fewer multipliers and six fewer adders than some well-known recursive algorithms. Therefore, the proposed architecture is better suited for various audio codecs.

Algebraic Signal Processing Theory: Sampling for Infinite and Finite 1-D Space

Abstract: We derive a signal processing framework, called space signal processing, that parallels time signal processing. As such, it comes in four versions (continuous/discrete, infinite/finite), each with its own notion of convolution and Fourier transform. As in time, these versions are connected by sampling theorems that we derive. In contrast to time, however, space signal processing is based on a different notion of shift, called space shift, which operates symmetrically. Our work rigorously connects known and novel concepts into a coherent framework; most importantly, it shows that the sixteen discrete cosine and sine transforms are the space equivalent of the discrete Fourier transform, and hence can be derived by sampling. The platform for our work is the algebraic signal processing theory, an axiomatic approach and generalization of linear signal processing that we recently introduced.

FPGA implementation of discrete fractional Fourier transform

Abstract: Since decades, fractional Fourier transform has taken a considerable attention for various applications in signal and image processing domain. On the evolution of fractional Fourier transform and its discrete form, the real time computation of discrete fractional Fourier transform is essential in those applications. On this context, we have proposed new hardware architecture for implementing a Discrete Fractional Fourier Transform (DFrFT) which requires hardware complexity of O(4N), where N is transform order. This proposed architecture has been simulated and synthesized using verilogHDL, targeting a FPGA device (XLV5LX110T). The simulation results are very close to the results obtained by using MATLAB. The result shows that, this architecture can be operated on a maximum frequency of 217MHz.

Encryption of speech signal with multiple secret keys in time and transform domains

Abstract: This paper introduces a new speech cryptosystem, which is based on permutation and masking of speech segments using multiple secret keys in both time and transform domains. The main key is generated, randomly, using a Pseudo Noise (PN) sequence generator, and two other keys are generated from the main key to be used in the subsequent rounds of encryption. Either the Discrete Cosine Transform (DCT) or the Discrete Sine Transform (DST) can be used in the proposed cryptosystem to remove the residual intelligibility resulting from permutation and masking in the time domain. In the proposed cryptosystem, the permutation process is performed with circular shifts calculated from the key bits. The utilized mask is also generated from the secret key by circular shifts. The proposed cryptosystem has a low complexity, small delay, and high degree of security. Simulation results prove that the proposed cryptosystem is robust to the presence of noise.

Recovering Missing Slices of the Discrete Fourier Transform using Ghosts

Abstract: The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information This incomplete coverage of Fourier space always produces systematic artefacts called Ghosts In this paper, a fast and exact method for de-convolving cyclic artefacts caused by missing slices of the DFT is presented The slices discussed here originate from the exact partitioning of DFT space, under the projective Discrete Radon Transform, called the Discrete Fourier Slice Theorem The method has a computational complexity of O(n log2 n) (where n = N^2) and is constructed from a new Finite Ghost theory This theory is also shown to unify several aspects of work done on Ghosts over the past three decades The paper concludes with a significant application to fast, exact, non-iterative image reconstruction from sets of discrete slices obtained for a limited range of projection angles

A low complexity orthogonal 8×8 transform matrix for fast image compression

Abstract: In this paper, an efficient orthogonal sparse 8×8 transform matrix for low bit-rate image compression is proposed. The transform matrix is made sparse by appropriately inserting additional zeros into the matrix proposed by Bouguezel. The algorithm for fast computation is also developed. It is shown that the proposed transform matrix provides a 20% reduction in computation over the matrix proposed by Bouguezel, and 45% over signed discrete cosine transform (SDCT). By using various test images, it is shown that the rate-distortion performance is also almost comparable to that of above two transform matrices at low bit-rates.

Two-dimensional simulation of Rayleigh waves with staggered sine/cosine transforms and variable grid spacing

Abstract: Simulation of Rayleigh waves requires high accuracy and an adequate spatial sampling at the surface. Discrete cosine and sine transforms are used to compute spatial derivatives along the direction perpendicular to the surface of the earth. Unlike the standard Fourier method, these transforms allow nonperiodicboundaryconditionstobesatisfied,inparticular, the stress-free conditions at the surface. Because simulation of surface waves requires more points per minimum wavelengthatthesurfacethansimulationofbodywaves,theequispaced grid is not efficient.To overcome this problem, a grid compression is performed at the surface to obtain a denser spatial sampling. Grid size is minimal at the surface and increases with depth until reaching, at a relatively shallow depth, the grid points per wavelength required by the body waves. The stress-free boundary conditions are naturally handled by expanding the appropriate stress components in terms of the discrete sine transform. The wave equation is solved in the particle-velocity and stress formulation using a Runge-Kutta time integration and the convolutional PML CPMLmethodtopreventreflectionsfromthemeshboundaries. The simulations are very accurate for shallow sources andreceiversandlargeoffsets.

All-Optical Discrete Fourier Transform Based On Multimode Interference Couplers

Abstract: In this letter, an all-optical discrete Fourier transform (DFT) device based on multimode interference (MMI) couplers is proposed. The DFT device is composed of a discrete sine transform device and a discrete cosine transform device, both of which are based on MMI couplers. The main advantage of this DFT device is that it is composed of two compact MMI couplers, which greatly reduces the fabrication effort on planar lightwave circuits.

Autoregressive Modeling of Temporal/Spectral Envelopes With Finite-Length Discrete Trigonometric Transforms

Abstract: The theory of autoregressive (AR) modeling, also known as linear prediction, has been established by the Fourier analysis of infinite discrete-time sequences or continuous-time signals. Nevertheless, for various finite-length discrete trigonometric transforms (DTTs), including the discrete cosine and sine transforms of different types, the theory is not well established. Several DTTs have been used in current audio coding, and the AR modeling method can be applied to reduce coding artifacts or exploit data redundancies. This paper systematically develops the AR modeling fundamentals of temporal and spectral envelopes for the sixteen members of the DTTs. This paper first considers the AR modeling in the generalized discrete Fourier transforms (GDFTs). Then, we derive the modeling to all the DTTs by introducing the analytic transforms which convert the real-valued vectors into complex-valued ones. Through the process, we build the compact matrix representations for the AR modeling of the DTTs in both time domain and DTT domain. These compact forms also illustrate that the AR modeling for the envelopes can be performed through the Hilbert envelope and the power envelope. These compact forms can be used to develop new coding technologies or examine the possible defects in the existing AR modeling methods for DTTs, We apply the forms to analyze the current temporal noise shaping (TNS) tool in MPEG-2/4 advanced audio coding (AAC).

Orbital Algorithms and Unified Array Processor for Computing 2D Separable Transforms

Abstract: The two-dimensional (2D) forward/inverse discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), discrete Walsh-Hadamard transform (DWHT), play a fundamental role in many practical applications. Due to the separability property, all these transforms can be uniquely defined as a triple matrix product with one matrix transposition. Based on a systematic approach to represent and schedule different forms of the $n\times n$ matrix-matrix multiply-add (MMA) operation in 3D index space, we design new orbital highly-parallel/scalable algorithms and present an efficient $n\times n$ unified array processor for computing {\it any} $n\times n$ forward/inverse discrete separable transform in the minimal $2n$ time-steps. Unlike traditional 2D systolic array processing, all $n^2$ register-stored elements of initial/intermediate matrices are processed simultaneously by all $n^2$ processing elements of the unified array processor at each time-step. Hence the proposed array processor is appropriate for applications with naturally arranged multidimensional data such as still images, video frames, 2D data from a matrix sensor, etc. Ultimately, we introduce a novel formulation and a highly-parallel implementation of the frequently required matrix data alignment and manipulation by using MMA operations on the same array processor so that no additional circuitry is needed.