Showing papers on "Discrete sine transform published in 2005"

Fast numerical algorithm for the linear canonical transform.

Abstract: The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an NlogN algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.

On the multiangle centered discrete fractional Fourier transform

Abstract: Existing versions of the discrete fractional Fourier transform (DFRFT) are based on the discrete Fourier transform (DFT). These approaches need a full basis of DFT eigenvectors that serve as discrete versions of Hermite-Gauss functions. In this letter, we define a DFRFT based on a centered version of the DFT (CDFRFT) using eigenvectors derived from the Gru/spl uml/nbaum tridiagonal commutor that serve as excellent discrete approximations to the Hermite-Gauss functions. We develop a fast and efficient way to compute the multiangle version of the CDFRFT for a discrete set of angles using the FFT algorithm. We then show that the associated chirp-frequency representation is a useful analysis tool for multicomponent chirp signals.

Systolic algorithms and a memory-based design approach for a unified architecture for the computation of DCT/DST/IDCT/IDST

Abstract: In this paper, an efficient design approach for a unified very large-scale integration (VLSI) implementation of the discrete cosine transform/discrete sine transform/inverse discrete cosine transform/inverse discrete sine transform based on an appropriate formulation of the four transforms into cyclic convolution structures is presented. This formulation allows an efficient memory-based systolic array implementation of the unified architecture using dual-port ROMs and appropriate hardware sharing methods. The performance of the unified design is compared to that of some of the existing ones. It is found that the proposed design provides a superior performance in terms of the hardware complexity, speed, I/O costs, in addition to such features as regularity, modularity, pipelining capability, and local connectivity, which make the unified structure well suited for VLSI implementation.

Low-error carry-free fixed-width multipliers with low-cost compensation circuits

Abstract: In this paper, we propose a low-error fixed-width redundant multiplier design. The design is based on the statistical analysis of the error compensation value of the truncated partial products in binary signed-digit representation with modified Booth encoding. The overall truncation error is significantly reduced compared with other previous approaches. Furthermore, the derived relationship between the compensation value and the truncated digits is so simple that the area cost of the corresponding compensation circuit is almost negligible. The fixed-width multiplier design is also applied to the discrete cosine transform/inverse discrete cosine transform (DCT/IDCT) computation in JPEG image compression.

Coding with improved time resolution for selected segments via adaptive block transformation of a group of samples from a subband decomposition

Abstract: A transform coder is described that performs a time-split transform in addition to a discrete cosine type transform. A time-split transform is selectively performed based on characteristics of media data. Transient detection identifies a changing signal characteristic, such as a transient in media data. After encoding an input signal from a time domain to a transform domain, a time-splitting transformer selectively perform an orthogonal sum-difference transform on adjacent coefficients indicated by a changing signal characteristic location. The orthogonal sum-difference transform on adjacent coefficients results in transforming a vector of coefficients in the transform domain as if they were multiplied by an identity matrix including at least one 2×2 time-split block along a diagonal of the matrix. A decoder performs an inverse of the described transforms.

The discrete Pascal transform and its applications

Abstract: We introduce a new discrete polynomial transform constructed from the rows of Pascal's triangle. The forward and inverse transforms are computed the same way in both the one- and two-dimensional cases, and the transform matrix can be factored into binary matrices for efficient hardware implementation. We conclude by discussing applications of the transform in digital image processing, such as bump and edge detection.

The fast Fourier transform for experimentalists. Part I. Concepts

Abstract: The discrete Fourier transform (DFT) provides a means for transforming data sampled in the time domain to an expression of this data in the frequency domain. The inverse transform reverses the process, converting frequency data into time-domain data. Such transformations can be applied in a wide variety of fields, from geophysics to astronomy, from the analysis of sound signals to CO/sub 2/ concentrations in the atmosphere. Over the course of three articles, our goal is to provide a convenient summary that the experimental practitioner will find useful. In the first two parts of this article, we'll discuss concepts associated with the fast Fourier transform (FFT), an implementation of the DFT. In the third part, we'll analyze two applications: a bat chirp and atmospheric sea-level pressure differences in the Pacific Ocean.

Quantum circuit design of 8/spl times/8 discrete cosine transform using its fast computation flow graph

Abstract: In this paper, the quantum circuit design of an 8/spl times/8 discrete cosine transform (DCT) is investigated. The proposed design procedure can be divided into the following three steps. First, the DCT matrix is decomposed into the product of sparse matrices, based on its fast computation flow graph. Second, each sparse matrix is implemented by elementary quantum gates. Third, the sparse matrix circuits are cascaded to obtain the final circuit. The proposed method makes the fast DCT computation algorithm in digital signal processing suitable for implementation in a quantum computer.

Warped discrete cosine transform-based noisy speech enhancement

Abstract: In this paper, a warped discrete cosine transform (WDCT)-based approach to enhance the degraded speech under background noise environments is proposed. For developing an effective expression of the frequency characteristics of the input speech, the variable frequency warping filter is applied to the conventional discrete cosine transform (DCT). The frequency warping control parameter is adjusted according to the analysis of spectral distribution in each frame. For a more accurate analysis of spectral characteristics, the split-band approach in which the global soft decision for speech presence is performed in each band separately is employed. A number of subjective and objective tests show that the WDCT-based enhancement method yields better performance than the conventional DCT-based algorithm.

An image compression scheme based on parametric Haar-like transform

Abstract: A new image compression scheme is presented, based on a fast orthogonal parametrically adaptive Haar-like transform, which is a discrete orthogonal transform such that it may be computed with a fast algorithm in structure similar to the classical fast Haar transform, and such that its matrix contains one or more predefined row(s) of an arbitrary order. The nature of the proposed image compression scheme is such that its performance (in terms of PSNR versus compression ratio) cannot be worse than that of the classical DCT (discrete cosine transform) based scheme. Simulations show that a significant performance improvement can be achieved for certain types of images such as medical X-ray images.

Interferometric Phase-Measurement Using a One-Dimensional Discrete Hilbert Transform

Abstract: A phase demodulation scheme using a discrete Hilbert transform that can change the interferometric phase by π/2 has been investigated. In-quadrature components of a fringe pattern are obtained from one captured interferogram using a one-dimensional (1-D) discrete Hilbert transform and a 1-D discrete high-pass filtering that are based on a digital signal processing technique. The phase distribution in the range of 15π (rad) can be demodulated with the proposed method. The 1-D discrete Hilbert transform can be extended to two-dimensional calculation with a raster scanning procedure. © 2005 The Optical Society of Japan

Frequency responses and resolving power of numerical integration of sampled data.

Abstract: Methods of numerical integration of sampled data are compared in terms of their frequency responses and resolving power. Compared, theoretically and by numerical experiments, are trapezoidal, Simpson, Simpson-3/8 methods, method based on cubic spline data interpolation and Discrete Fourier Transform (DFT) based method. Boundary effects associated with DFT- based and spline-based methods are investigated and an improved Discrete Cosine Transform based method is suggested and shown to be superior to all other methods both in terms of approximation to the ideal continuous integrator and of the level of the boundary effects.

Discrete fractional Fourier transform based on new nearly tridiagonal commuting matrices

Abstract: Based on discrete Hermite-Gaussian like functions, a discrete fractional Fourier transform (DFRFT) which provides sample approximations of the continuous fractional Fourier transform was defined and investigated recently. In this paper, we propose a new nearly tridiagonal matrix which commutes with the discrete Fourier transform (DFT) matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be better discrete Hermite-Gaussian like functions than those developed before. Furthermore, by appropriately combining two linearly independent matrices which both commute with the DFT matrix, we develop a method to obtain even better discrete Hermite-Gaussian like functions. Then, new versions of DFRFT produce their transform outputs more close to the samples of the continuous fractional Fourier transform, and their application is illustrated.

Influence of the boundary conditions on the result of non-linear image registration

Abstract: The focus of many non-parametric image registration algorithms lies on the solution of non-linear partial differential equations. We offer a simple solution procedure therefor based on discrete Fourier transform. Boundary conditions can strongly influence the result of the registration. The issue is investigated on the example of non-linear curvature-based registration.

Method of flow graph simplification for the 16-point discrete Fourier transform

Abstract: An efficient method for the realization of the paired algorithm for calculation of the one-dimensional (1-D) discrete Fourier transform (DFT), by simplifying the signal-flow graph of the transform, is described. The signal-flow graph is modified by separating the calculation for real and imaginary parts of all inputs and outputs in the signal-flow graph and using properties of the transform. The examples for calculation of the eight- and 16-point DFTs are considered in detail. The calculation of the 16-point DFT of real data requires 12 real multiplications and 58 additions. Two multiplications and 20 additions are used for the eight-point DFT.

Transform-based methods for indexing and retrieval of 3D objects

Abstract: We compare two transform-based indexing methods for retrieval of 3D objects. We apply 3D discrete Fourier transform (DFT) and 3D radial cosine transform (RCT) to the voxelized data of 3D objects. Rotation invariant features are derived from the coefficients of these transforms. Furthermore we compare two different voxel representations, namely, binary denoting object and background space, and continuous after distance transformation. In the binary voxel representation the voxel values are simply set to 1 on the surface of the object and 0 elsewhere. In the continuous-valued representation the space is filled with a function of distance transform. The rotation invariance properties of the DFT and RCT schemes are analyzed. We have conducted retrieval experiments on the Princeton Shape Benchmark and investigated the retrieval performance of the methods using several quality measures.

Fourier transform for the spatial quincunx lattice

Abstract: We derive a new, two-dimensional nonseparable signal transform for computing the spectrum of spatial signals residing on a finite quincunx lattice. The derivation uses the connection between transforms and polynomial algebras, which has long been known for the discrete Fourier transform (DFT), and was extended to other transforms in recent research. We also show that the new transform can be computed with O(n/sup 2/ log(n)) operations, which puts it in the same complexity class as its separable counterparts.

Haar wavelet transform embedded lossless type II discrete cosine transform

Abstract: A shared lossless Haar transform and an appended discrete cosine transform type-II are combined to form a discrete cosine type-II transform in a parallel pipelined architecture for providing lossless data transformation.

Performance evaluation of 3-D transforms for medical image compression

Abstract: In this paper, 3-D discrete Hartley, cosine and Fourier transforms are used for the compression of magnetic resonance images and X-ray angiograms. The performance results are then compared and evaluated. The transforms are applied on image blocks of sizes 8times8timesM where M represents the number of slices. The resultant transform coefficients are quantized and then encoded using a combination of run length and Huffman coding schemes to achieve maximum compression. The performances of the transforms are evaluated in terms of peak signal to noise ratio and bit rate. It is found from the experimental results, that 3-D discrete Hartley transform yields the best results for magnetic resonance brain images whereas for X-ray angiograms the 3-D discrete cosine transform is found to be superior to the other two transforms

Fourier transform for the directed quincunx lattice

Abstract: We introduce a new signal transform for computing the spectrum of a signal given on a two-dimensional directional quincunx lattice. The transform is non-separable, but closely related to a two-dimensional (separable) discrete Fourier transform. We derive the transform using recently discovered connections between signal transforms and polynomial algebras. These connections also yield several important properties of the new transform.

Method and system for fast implementation of an approximation of a discrete cosine transform

Abstract: A processor includes a multi-stage pipeline having a plurality of stages. Each stage is capable of receiving input values and providing output values. Each stage performs one of a plurality of data transformations using the input values to produce the output values. The data transformations collectively approximate at least one of: a discrete cosine transform and an inverse discrete cosine transform. The stages do not use any multipliers to perform the data transformations.

Modified ICA algorithms for finding optimal transforms in transform coding

Abstract: In this paper we present two new algorithms that compute the linear optimal transform in high-rate transform coding, for non Gaussian data. One algorithm computes the optimal orthogonal transform, and the other the optimal linear transform. Comparison of the performances in high-rate transform coding between the classical Karhunen-Loeve Transform (KLT) and the transforms returned by the new algorithms are given. On synthetic data, the transforms given by the new algorithms perform significantly better that the KLT, however on real data all the transforms, included KLT, give roughly the same coding gain.

Low computation cycle and high speed recursive DFT/IDFT: VLSI algorithm and architecture

Abstract: In this paper, we propose two low-computation cycle and high-speed recursive discrete Fourier transform (DFT)/inverse DFT (IDFT) architectures adopting the hybrid of Chebyshev polynomial and register-splitting scheme. The proposed core-type recursive architecture achieves half computation-cycle reduction as well as less critical period compared with the conventional second-order DFT/IDFT architecture. So as to further reduce the number of computation cycles, based on the new core-type design, we develop the folded-type recursive DFT/IDFT architecture with the same operating frequency. Moreover, from the derivation results, the operation of DFT and IDFT can be performed with the same structure under different configurations.

On unified architectures for synthesizing and implementation of fast parametric transforms

Abstract: In this paper a methodology to design VLSI architectures for parametric transform families is proposed. A parametric transform family consists of discrete orthogonal transforms such that they all may be computed with a fast algorithm of similar structure where parameters defining the transform within the family are used. In our previous work, an algorithm to synthesize transforms with predefined basis functions was introduced and efficiently applied to image compression. The methodology proposed in this paper allows of designing VLSI architectures that may not only switch from one transform of a family to another by setting parameters, but also to actually set these parameters so that the matrix of the resulting transform has predefined basis functions

A fast and accurate inverse discrete cosine transform

Abstract: The discrete cosine transform (DCT) is a widely used transform in image and video processing applications. By its mathematical definition, it is a computationally complex algorithm defined by cosine multiplications to accomplish the transformation of data to and from the frequency domain. Consequently, the fast implementation of the DCT is an active area of research as engineers endeavor to mitigate its complexity by approximating it with fixed-point algorithms. This paper presents a new design methodology for the design of linear transforms; the application of which introduces an example fixed-point inverse DCT implementation that is both fast and accurate, and complies with the specification in the IEEE Std. 1180 - 1990 (currently withdrawn).

Rapid update of odd DCT and DST for real-time signal processing

Abstract: When processing a signal or an image using the Discrete Cosine Transform (DCT) or Discrete Sine Transform (DST), a typical approach is to extract a portion of the signal by windowing and then form the DCT or DST of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. DCTs and DSTs are defined where the denominator in the transform kernel is either an odd or an even integer, resulting in transforms known as the even DCT (EDCT), even DST (EDST), odd DCT (ODCT) and odd DST (ODST). Each is available in types I to IV, for a total of 16 different transforms. The widely used transform commonly called the "DCT" is actually the EDCT-II. In this paper we extend our previous work using the EDCT-II and EDST-II, and show that a similar approach yields algorithms for the ODCT-II and ODST-II. We develop algorithms to "update" the ODCT-II and ODST-II simultaneously to reflect the modified window contents using less computation than directly evaluating the modified transform via standard Fast Transform algorithms. These algorithms are able to handle arbitrary step sizes up to the length of the transform, i.e. the algorithm simultaneously updates the ODCT-II and ODST-II to reflect inclusion of r, where 1 ≤ r ≤ N-1, additional data points and removal of r old points from the signal. Examples of applications where this algorithm would be useful include target recognition where time constraints may not permit the immediate processing of every incoming data point, adaptive system identification, etc.

Unified DA-based Parallel Architecture for Computing the DCT and the DST

Abstract: A common computing-core representation of the discrete cosine transform and discrete sine transform is derived, and a reduced-complexity algorithm is developed for computation of the proposed common computing-core A parallel architecture based on the principle of distributed arithmetic is designed further for computation of these transforms using the common-core algorithm The proposed scheme not only leads to a systolic-like, fully-pipelined regular and modular hardware for computing the these transforms, but also offers significant saving of hardware over the existing structures having nearly the same computational throughput The proposed structure is devoid of complicated input/output mapping and does not involve any complex control structure Moreover, it does not have restriction on the transform-length, and can be utilized as a reusable core for cost-effective, high-throughput implementation of either of these transforms