Showing papers on "Discrete sine transform published in 2009"

A test for second order stationarity of a time series based on the Discrete Fourier Transform (Technical Report)

Abstract: We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical frequencies. It is well known that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a type of noncentral chi-square, where the noncentrality parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power. Some real examples are also included to illustrate the test.

The Discrete Fourier Transform, Part 4: Spectral Leakage

Abstract: This paper is part 4 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 spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). We demonstrate an approach to mitigating spectral leakage based on windowing. Windowing temporally isolates the Short-Time Fourier Transform (STFT) in order to amplitude modulate the input signal. This requires that we know the extent, of the event in the input signal and that we have enough samples to yield a sufficient spectral resolution for our application. 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".

Brief Notes in Advanced DSP: Fourier Analysis with MATLAB

Abstract: Discrete Fourier Transform Properties of the discrete Fourier transform Fourier transform splitting Fast Fourier transform Codes for the paired FFT Paired and Haar transforms Integer Fourier Transform Reversible integer Fourier transform Lifting schemes for DFT One-point integer transform DFT in vector form Roots of the unit Codes for the block DFT General elliptic Fourier transforms Cosine Transform Partitioning the DCT Paired algorithm for the N-point DCT Codes for the paired transform Reversible integer DCT Method of nonlinear equations Canonical representation of the integer DCT Hadamard Transform The Walsh and Hadamard transform Mixed Hadamard transformation Generalized bit and transformations T-decomposition of Hadamard matrices Mixed Fourier transformations Mixed transformations: continuous case Paired Transform-Based Decomposition Decomposition of 1D signals 2D paired representation Fourier Transform and Multiresolution Fourier transform Representation by frequency-time wavelets Time-frequency correlation analysis Givens-Haar transformations References Index

Random Discrete Fractional Fourier Transform

Abstract: In this letter, a new commuting matrix with random discrete Fourier transform (DFT) eigenvectors is first constructed. A random discrete fractional Fourier transform (RDFRFT) kernel matrix with random DFT eigenvectors and eigenvalues is then proposed. The RDFRFT has an important feature that the magnitude and phase of its transform output are both random. As an application example, a security-enhanced image encryption scheme based on the RDFRFT is illustrated.

Method and apparatus for encoding and decoding transform coefficients

Abstract: A method of encoding transform coefficients and a transform coefficient encoding apparatus, and a method of decoding transform coefficients and a transform coefficient decoding apparatus are provided. The method of encoding the transform coefficients includes reading transform coefficients in a current block, determining whether a first transform coefficient having an absolute value greater than a predetermined threshold value exists in the transform coefficients in the current block, generating first flag information indicating whether the first transform coefficient exists, dividing the first transform coefficient from information of a second transform coefficient that is remaining transform coefficients excluding the first transform coefficient, and encoding the first transform coefficients and the second transform coefficients separately, thereby more efficiently using a correlation between each of the transform coefficients.

Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform

Abstract: A new transform known as conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) is presented in this paper. The transform matrix of this transform possesses sequency ordering and the spectrum obtained by the CS-SCHT is conjugate symmetric. Some of its important properties are discussed and analyzed. Sequency defined in the CS-SCHT is interpreted as compared to frequency in the discrete Fourier transform. The exponential form of the CS-SCHT is derived, and the proof of the dyadic shift invariant property of the CS-SCHT is also given. The fast and efficient algorithm to compute the CS-SCHT is developed using the sparse matrix factorization method and its computational load is examined as compared to that of the SCHT. The applications of the CS-SCHT in spectrum estimation and image compression are discussed. The simulation results reveal that the CS-SCHT is promising to be employed in such applications.

Real-time fluid simulation using discrete sine/cosine transforms

Abstract: Recent advances in fluid simulations have yielded exceptionally realistic imagery However, most algorithms have computational requirements that are prohibitive for real-time simulations Using Fourier based solutions mitigates this issue, although due to wraparound, boundary conditions are not naturally available, leading to inconsistencies near the boundary We show that slip boundary conditions can be imposed by solving the mass conservation step using cosine and sine transforms instead of the Fourier transform Further, we show that measures against density dissipation can be computed using cosine transforms and we describe a new method to compute surface tension in the same domain This combination of related algorithms leads to real-time simulations with boundary conditions

A spectral 1st level FPGA trigger for detection of very inclined showers based on a 16-point discrete cosine transform for the Pierre Auger Observatory

Abstract: The paper describes a new spectral trigger based on the 16-point discrete cosine transform (DCT) algorithm that was implemented into an FPGA. The DCT trigger allows recognition of FADC traces with a very short rise time and fast exponential attenuation related to a narrow, flat muon component of very inclined extensive air showers generated by hadrons and starting their development early in the atmosphere. The discrete cosine transform, based on only real coefficients in the frequency domain, provides much more sensitive trigger conditions and a simpler interpretation in comparison to a discrete Fourier transform (DFT) that is based on complex coefficients or their absolute values. It also offers a scaling feature. The ratio of the DCT coefficients to the 1st harmonics depends only on the shape of signals, not on their amplitudes. However, an implementation of the DCT into an FPGA requires more resources than DFT even based on an FFT algorithm.

Robust color texture features based on ranklets and discrete Fourier transform

Abstract: We present a set of multiscale, multidirectional, rotation-invariant features for color texture characterization. The proposed model is based on the ranklet transform, a technique relying on the calculation of the relative rank of the intensity level of neighboring pixels. Color and texture are merged into a compact descriptor by computing the ranklet transform of each color channel separately and of couples of color channels jointly. Robustness against rotation is based on the use of circularly symmetric neighborhoods together with the discrete Fourier transform. Experimental results demonstrate that the approach shows good robustness and accuracy.

Some accelerated flows of generalized Oldroyd-B fluid between two side walls perpendicular to the plate

Abstract: This paper deals with some accelerated flows of generalized Oldroyd-B fluid between two side walls perpendicular to the plate. The fractional calculus approach is used in the constitutive relationship of the Oldroyd-B fluid. The exact analytic solution is obtained by means of mixed Fourier sine transform and discrete Laplace transform for fractional derivative.

Generalized Discrete Cosine Transform

Abstract: The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. Finally, a new type of discrete cosine transform is proposed and its orthogonality is proved.

A Fast Fourier Transform with Rectangular Output on the BCC and FCC Lattices

Abstract: This paper discusses the efficient, non-redundant evaluation of a Discrete Fourier Transform on the three dimensional Body-Centered and Face-Centered Cubic lattices. The key idea is to use an axis aligned window to truncate and periodize the sampled function which leads to separable transforms. We exploit the geometry of these lattices and show that by choosing a suitable non-redundant rectangular region in the frequency domain, the transforms can be efficiently evaluated using the Fast Fourier Transform.

Chaotic image encryption in transform domains

Abstract: This paper presents a new approach for image encryption based on the chaotic Baker map, but in the different transform domains. The discrete cosine transform (DCT), the discrete sine transform (DST), the discrete wavelet transform (DWT) and the additive wavelet transform (AWT) are exploited in the proposed encryption approach. Chaotic encryption is performed in these transform domains to make use of the characteristics of each domain. A comparison study between all transform domain encryption schemes is held in the presence of different attacks. Results of this comparison study are in favor of encryption in the DST domain if the degree of randomness is of major concern.

A space-vector discrete Fourier transform for detecting harmonic sequence components of three-phase signals

Abstract: In this paper, a discrete-time algorithm for separately detecting the positive- and negative-sequence harmonic space-vector components of a three-phase signal is presented The discrete Fourier transform is applied to the three-phase signals represented by the Clarke's as vector The proposed transform outputs the instantaneous values of the fundamental frequency and harmonic component vectors of the input three-phase signals A recursive algorithm for low-effort online implementation is also presented The detection performance for variable frequency and inter-harmonic input signals is discussed The proposed method performance is verified through experiments

Rate-distortion optimized adaptive transform coding

Abstract: We propose a rate-distortion optimized transform coding method that adaptively employs either integer cosine transform that is an integer-approximated version of discrete cosine transform (DCT) or integer sine transform (IST) in a rate-distortion sense The DCT that has been adopted in most video-coding standards is known as a suboptimal substitute for the Karhunen-Loeve transform However, according to the correlation of a signal, an alternative transform can achieve higher coding efficiency We introduce a discrete sine transform (DST) that achieves the high-energy compactness in a correlation coefficient range of −05 to 05 and is applied to the current design of H264/AVC (advanced video coding) Moreover, to avoid the encoder and decoder mismatch and make the implementation simple, an IST that is an integer-approximated version of the DST is developed The experimental results show that the proposed method achieves a Bjontegaard Delta-RATE gain up to 549% compared to Joint model 110

Image processing using spatial transform

Abstract: This paper deals with image processing using spatial (geometric) transforms such as translation, rotation, and scaling, shearing, and projective transform. These transforms can be used for image correction. Translation, rotation, and scaling transform are also called affine transform which is a subset of projective transform. All the methods are given experimental results implemented in Matlab.

Chapter 6 – Feature Generation I: Data Transformation and Dimensionality Reduction

Abstract: Publisher Summary This chapter discusses the feature generation stage using data transformations and dimensionality reduction. Feature generation is important in any pattern recognition task. Given a set of measurements, the goal is to discover compact and informative representations of the obtained data. The basic approach followed in this chapter is to transform a given set of measurements to a new set of features. If the transform is suitably chosen, transform domain features can exhibit high information packing properties compared with the original input samples. The chapter reviews Karhunen–Loeve transform and the singular value decomposition as dimensionality reduction techniques. The independent component analysis, nonnegative matrix factorization, and nonlinear dimensionality reduction techniques are presented. Then the discrete Fourier transform, discrete cosine transform, discrete sine transform, Hadamard, and Haar transforms are defined. The rest of the chapter focuses on the discrete time wavelet transform. The chapter also shows that the Fourier transform is just one of the tools from a palette of possible transforms.

A Discrete Fourier Transform Framework for Localization Relations

Abstract: Localization relations arise naturally in the formulation of multi-scale models. They facilitate statistical analysis of local phenomena that may contribute to failure related properties. The computational burden of dealing with such relations is high and recent work has focused on spectral methods to provide more efficient models. Issues with the inherent integrations in the framework have led to a tendency towards calibration-based approaches. In this paper a discrete Fourier transform framework is introduced, leading to an extremely efficient basis for the localization relations. Previous issues with the Green’s function integrals are resolved, and the method is validated against finite element analysis.

A New Decomposition Algorithm of DCT-IV/DST-IV for Realizing Fast IMDCT Computation

Abstract: In this letter, a new decomposition algorithm of type-IV discrete cosine transform/type-IV discrete sine transform (DCT-IV/DST-IV) and architecture of a hardware accelerator for realizing fast inverse modified discrete cosine transform (IMDCT) computation are presented. The comparisons of computational complexity with some well-known algorithms show that the proposed algorithm possesses the advantages of higher computational efficiency and simpler hardware implementation. A real-time audio decoding experiment was performed to verify the efficiency of the proposed algorithm. Experimental results show more than one third of computational cycles are saved compared with one of reported fast algorithms for IMDCT computation.

A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum estimation

Abstract: We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb–Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations.

The Basic Discrete Hilbert Transform with an Information Hiding Application

Abstract: This paper presents several experimental findings related to the basic discrete Hilbert transform. The errors in the use of a finite set of the transform values have been tabulated for the more commonly used functions. The error can be quite small and, for example, it is of the order of 10^{-17} for the chirp signal. The use of the discrete Hilbert transform in hiding information is presented.

Discrete integer Fourier transform in real space: elliptic Fourier transform

Abstract: The concept of the N -point DFT is generalized, by considering it in the real space (not complex). The multiplication by twiddle coefficients is considered in matrix form; as the Givens transformation. Such block-wise representation of the matrix of the DFT is effective. The transformation which is called the T -generated N -block discrete transform, or N -block T-GDT is introduced. For each N -block T-GDT, the inner product is defined, with respect to which the rows (and columns) of the matrices X are orthogonal. By using different parameterized matrices T , we define metrics in the real space of vectors. The selection of the parameters can be done among only the integer numbers, which leads to integer-valued metric. We also propose a new representation of the discrete Fourier transform in the real space R 2N . This representation is not integer, and is based on the matrix C (2x2) which is not a rotation, but a root of the unit matrix. The point (1, 0) is not moving around the unite circle by the group of motion generated by C, but along the perimeter of an ellipse. The N -block C-GDT is therefore called the N -block elliptic FT (EFT). These orthogonal transformations are parameterized; their properties are described and examples are given.

The Discrete Cosine Transform DCT

Abstract: The Fourier transform and the DFT are designed for processing complex-valued signals, and they always produce a complex-valued spectrum even in the case where the original signal was strictly realvalued. The reason is that neither the real nor the imaginary part of the Fourier spectrum alone is sufficient to represent (i.e., reconstruct) the signal completely. In other words, the corresponding cosine (for the real part) or sine functions (for the imaginary part) alone do not constitute a complete set of basis functions.