Showing papers on "Discrete sine transform published in 2018"

An efficient computational approach for time-fractional Rosenau–Hyman equation

Abstract: In this work, we concentrate on the analysis of the time-fractional Rosenau–Hyman equation occurring in the formation of patterns in liquid drops via q-homotopy analysis transform technique and reduced differential transform approach. The q-homotopy analysis transform algorithm can provide rapid convergent series by choosing the appropriate values of auxiliary parameters ħ and n at large domain. The reduced differential transform technique gives wider applicability due to reduction in computations and makes the calculation much simpler and easier. The proposed techniques are realistic and free from any assumption and perturbation for solving the time-fractional Rosenau–Hyman equation.

A nonuniform fast Fourier transform based on low rank approximation

Abstract: By viewing the nonuniform discrete Fourier transform (NUDFT) as a perturbed version of a uniform discrete Fourier transform, we propose a fast and quasi-optimal algorithm for computing the NUDFT based on the fast Fourier transform (FFT). Our key observation is that an NUDFT and DFT matrix divided entry by entry is often well approximated by a low rank matrix, allowing us to express a NUDFT matrix as a sum of diagonally scaled DFT matrices. Our algorithm is simple to implement, automatically adapts to any working precision, and is competitive with state-of-the-art algorithms. In the fully uniform case, our algorithm is essentially the FFT. We also describe quasi-optimal algorithms for the inverse NUDFT and two-dimensional NUDFTs.

Hardware Design and Implementation of Adaptive Multiple Transforms for the Versatile Video Coding Standard

Abstract: Versatile video coding is the next generation video coding standard expected by the end of 2020. Several new contributions have been proposed to enhance the coding efficiency beyond the high efficiency video coding standard. One of these tools is the adaptive multiple transform (AMT) as a new approach of the transform core design. The AMT involves five discrete cosine transform/discrete sine transform types with larger and more flexible partitioning block sizes. However, the AMT coding efficiency comes with the cost of higher computational complexity, especially at the encoder side. In this paper, a efficient pipelined hardware implementation of the AMT including the five types of sizes $4\times 4$ , $8\times 8$ , $16\times 16$ and $32\times 32$ is proposed. The architecture design takes advantage of the internal software/hardware resources of the target field-programmable gate array device such as library of parametrized modules core intellectual properties and digital signal processing blocks. The proposed 1-D 32-point AMT design allows to process 4K video at 44 frames/s. A unified 2-D implementation of the 4, 8, 16, and 32-point AMT design is also presented.The implementation takes into account all the asymmetric 2-D block size combinations from 4 to 32. The 2-D architecture design is able to sustain 2K video coding at 50 frames/s with an operational frequency up to 147 MHz.

A Robust and Improved Visual Quality Data Hiding Method for HEVC

Abstract: This paper presents a novel and robust data hiding method based on H.265 /High Efficiency Video Coding ( HEVC ) standard. To improve the robustness of data hiding, the embedded data are first encoded into the encoded data by using the BCH syndrome code ( BCH code ) technique. To improve the visual quality of data hiding, three groups of the prediction directions are provided to limit the intra-frame distortion drift. Then, the encoded data are embedded into the multi-coefficients of the selected $4 \times 4$ luminance discrete sine transform blocks, which meet the groups. It is experimentally proven that the proposed method can achieve greater robustness, better visual quality, and higher embedding capacity than previously studied methods.

An efficient lossless robust watermarking scheme by integrating redistributed invariant wavelet and fractional Fourier transforms

Abstract: An ensemble lossless watermarking scheme is proposed in the present study by integrating different concepts like redistributed invariant wavelet transform, discrete fractional Fourier transform, singular value decomposition (SVD) and visual cryptography within the framework of a single algorithm The invariant wavelet transform helps to obtain the transform domain, which is invariant to flipping and rotation of image, this is followed by discrete fractional Fourier transform to obtain the translation invariant domain Finally, embedding positions are selected based on a key and reliable features are extracted by performing SVD on a window centered at these positions Based on these reliable features a binary map is generated through which a master share is created The corresponding ownership share is produced from the master share and the watermark In verification process the same operations of the embedding process are applied to the test image to obtain the master share and the watermark is recovered by stacking it over the ownership share There are two main features of the proposed scheme (1) The quality of the image to be watermarked do not degrade during the process and (2) the extracted watermark can still be identified even from a seriously distorted image These findings are also demonstrated with the help of a comparative study with several related schemes

A Fast Algorithm for Solving the Space-Time Fractional Diffusion Equation

Abstract: In this paper, we propose a fast algorithm for efficient and accurate solution of the space–time fractional diffusion equations defined in a rectangular domain. The spatial discretization is done by using the central finite difference scheme and matrix transfer technique. Due to its nonlocality, numerical discretization of the spectral fractional Laplacian ( − Δ ) s α / 2 results in a large dense matrix. This causes considerable challenges not only for storing the matrix but also for computing matrix–vector products in practice. By utilizing the compact structure of the discrete system and the discrete sine transform, our algorithm avoids to store the large matrix from discretizing the nonlocal operator and also significantly reduces the computational costs. We then use the Laplace transform method for time integration of the semi-discretized system and a weighted trapezoidal method to numerically compute the convolutions needed in the resulting scheme. Various experiments are presented to demonstrate the efficiency and accuracy of our method.

The eigenstructures of real (skew) circulant matrices with some applications

Abstract: The circulant matrices and skew-circulant matrices are two special classes of Toeplitz matrices and play vital roles in the computation of Toeplitz matrices. In this paper, we focus on real circulant and skewcirculant matrices. We first investigate their real Schur forms, which are closely related to the family of discrete cosine transform (DCT) and discrete sine transform (DST). Using those real Schur forms, we then develop some fast algorithms for computing real circulant, skew-circulant and Toeplitz matrix-real vector multiplications. Also, we develop a DCT-DST version of circulant and skew-circulant splitting (CSCS) iteration for real positive definite Toeplitz systems. Compared with the fast Fourier transform (FFT) version of CSCS iteration, the DCTDST version is more efficient and saves a half storage. Numerical experiments are presented to illustrate the effectiveness of our method.

HEVC transforms with reduced elements bit depth

Abstract: High-efficiency video coding (HEVC) is based on integer discrete cosine transforms (DCTs) of size 4 × 4, 8 × 8, 16 × 16 and 32 × 32 whose elements are coded on 8 bits However, the algorithm requires that the output length at each processing stage should never exceed 16 bits The conventional solution is the truncation of the least significant bits which leads to erroneous results and a waste of resources In this Letter, different DCT kernels with reduced elements length are proposed They are evaluated for compression efficiency and hardware implementation competence An implementation on the Xilinx FPGA virtex-6 circuit has given a maximal operating frequency increase of 481 and 9341% for the DCT-II 4 × 4 and the discrete sine transform, while reducing the energy consumption by 1064 and 3077% at 100 MHz, respectively Using the HM 163 HEVC model and video sequences of different resolutions, the results show a quality degradation of 001 dB for a bit rate increase of 019% compared to the reference cores

QIM-Based Audio Watermarking with Combined Techniques of SWT-DST-QR-CPT Using SS-Based Synchronization

Abstract: Audio watermarking is a technique of inserting information into an audio file so humans are not aware of the existence of such additional information. In this paper, we propose synchronization of audio watermarking with Quantization Index Modulation (QIM) with combined techniques of Stationary Wavelet Transform (SWT), Discrete Sine Transform (DST), QR Decomposition, and Cartesian Polar Transform (CPT). Firstly, after reading host audio, we insert header using SS-based synchronization. Next, host audio is decomposed by SWT, then several subbands with average power above than threshold are selected for next process. Next, the selected subbands in time domain are transformed by DST into frequency domain. Then, the frequency domain signal is decomposed by QR decomposition. In R matrix, its coefficients at position (1,1) and (2.2) are transformed using CPT. Finally, QIM inserts watermark bits into CPT coefficients. Watermarking scheme has an average SNR value of 32.718 dB and 82.61% success rate in Stirmark Benchmarck for Audio (SMBA) as standard attack for audio watermarking with $\mathbf{BER} < 10\%$.

Supercharacters and the discrete Fourier, cosine, and sine transforms

Abstract: Using supercharacter theory, we identify the matrices that are diagonalized by the discrete cosine and discrete sine transforms, respectively. Our method affords a combinatorial interpretation for ...

Explicit inversion of Band Toeplitz matrices by discrete Fourier transform

Abstract: In this paper, we give an explicit formula for the element of the inverse where is a band Toeplitz matrix with left bandwidth s and right bandwidth r. The formula involves determinants, , whose elements are the discrete Fourier transform of where f is the symbol of .

The Fourier Transform of a Function of Bounded Variation: Symmetry and Asymmetry

Abstract: New relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. The main result of the paper is an asymptotic formula for the cosine Fourier transform. Such relations have previously been known only for the sine Fourier transform. For this, not only a different space is considered but also a new way of proving such theorems is applied. Interrelations of various function spaces are studied in this context. The obtained results are used for obtaining completely new results on the integrability of trigonometric series.

Interpolation Filter Design Based on All-Phase DST and Its Application to Image Demosaicking

Abstract: Based on a deep understanding of all-phase digital filter (APDF) design and all-phase biorthogonal transform (APBT), this paper will further study the windowed all-phase digital filter (WAPDF) and windowed all-phase biorthogonal transform (WAPBT), discuss the principle of the WAPBT, and provide a unified construction method of the all-phase transform (APT). Based on a type of orthogonal transform, i.e., discrete sine transform (DST), an interpolation filter called an all-phase DST (APDST) filter is constructed and used for image demosaicking; it is compared with bilinear interpolation and all-phase inverse discrete cosine transform (APIDCT) interpolation filters, to test its performance in image interpolation and provide analysis and discussion. The experimental results show that APIDCT and APDST filters with a size of 7 × 7 are similar in interpolation performance, but better than the bilinear interpolation method. In addition to its use in image interpolation demosaicking, the low-pass filter designed in this paper can also be widely used in image interpolation, image denoising, image resizing, and other fields of image processing.

A Novel Waveform Design Based on Discrete Sine Transform for 5G and Beyond

Abstract: In this paper, it is proposed a new unique word (UW) OFDM waveform based on zero-tail discrete Sine transform spread OFDM (ZT UW DST-S OFDM). The proposed waveform improves the ZT DST-S-OFDM and UW OFDM methods by removing the influence of the data symbols on the tail of the transmitted signal. In this study, the effects of different UW sequences such as Zadoff-Chu, CAZAC, 15 bit PN, 8 bit complementary code keying (CCK), 0-word, 1-word and −1-word on the bit error rate (BER) and channel tracking (Doppler) performance of the proposed ZT UW DST-S OFDM systems are investigated. In order to test the performance of the proposed method, computer simulation studies are performed on time invariant and time variant frequency selective Rayleigh fading channels. The obtained results confirm that the proposed waveform has better BER and channel tracking (Doppler) performance than the conventional OFDM and ZT DFT-S OFDM systems. In particular, it is observed that the ZT UW DST-S OFDM using Zadoff-Chu sequence has the best BER and channel tracking performance.

CPT-Based Data Hiding in Selected Subband Using Combined Transform and Decomposition Method

Abstract: A digital copyright on an audio needs a special protection to prevent it from illegal distribution. Hiding a copyright into an audio is a solution for securing its ownership. In this paper, we propose an audio watermarking using combination method of Lifting Wavelet Transform (LWT), Discrete Sine Transform (DST), Singular Value Decomposition (SVD), and Cartesian Polar Transform (CPT) using Quantization Index Modulation (QIM). A host audio is first decomposed by LWT. Next, a subband is selected then transformed by DST. Then, DST selected coefficients are decomposed into U, S and V matrices by SVD. S matrix is then selected. S elements in position (1,1) and (2,2) are converted by CPT to magnitude and phase coefficients. The phase coefficient is finally used for embedding a bit of watermark by QIM. The simulation result shows that the proposed method offers very high watermark capacity with good imperceptibility and robustness.

Technique for Signal Noise Reduction based on Sparse Representation

Abstract: Noise is present in everyday life, that it is a fact to find it in everything. Depending on the applications, the noise can present or not issues. In sensing process, the noise would be a huge issue when the accuracy of the system is high, when the resolution of the sensor is better than, e.g., 40 mV/A. In this case, the outputs less than 3A have a high SNR. If these signals are used in signals processing, depending on its focus, they can provoke malfunctions and false positives. This paper presents, a methodology for noise reduction based on the sparse representation of a signal using a dictionary based on Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST). The proposed method is tested with synthetic signals to research its effectiveness, and then it is tested with real signals taken from the current that supply Induction Motors. After the methodology is applied, signals are analyzed to prove that the information contained is preserved. The noise reduction of the current signals was $\sim 30dB$ with the Motor under normal operating conditions.

Design and Implementation of Multi-Purpose DCT/DST-Specific Accelerator on Heterogeneous Multicore Architecture

Abstract: This paper presents the implementation of various sizes of Discrete Cosine transform (DCT) and Discrete Sine Transform (DST) dedicated for High Efficiency Video Coding (HEVC) standard by using template-based Coarse-Grained Reconfigurable Arrays (CGRAs) as accelerators on Heterogeneous Accelerator-Rich Platform (HARP). The proposal makes multipurpose DCT/DST specific accelerators in such a way that final architecture consists of 4/8/16/32–point DCT and 4-point DST. The accelerators are primarily designed by crafting template-based CGRA devices at different dimensions and then arranging them on a Network-on-Chip platform along with a few RISC cores. In this research work, the performance of each DCT/DST-specific accelerator, the collective performance of the whole platform and the NoC traffic are recorded in terms of the number of clock cycles and several high-level performance metrics. Conducted experiments show that 4-point DCT and 4-point DST can be implemented completely in 54 and 56 clock cycles, respectively, while for 8/16/32–point DCT, 67, 179 and 354 clock cycles are required, respectively. The achieved total power dissipation and energy consumption based on post placement and routing information are equal to 4.1 W and $10.87~\mu {\mathrm {J}}$, respectively with 256 instantiated Processing Elements (PEs) at 200.0 MHz operating frequency. It resulted to a performance of 51.2 Giga Operations Per Second (GOPS) and 12 MOPS/mW as an architectural constant for the HARP template on 28 nm Altera Stratix-V chip. The proposed architecture is able to sustain Full HD 1080p format at 30 fps on FPGA.

Application of Discrete Sine Transform in Image Processing

Abstract: Digital devices & computational resources have limited communication & storage capabilities. Because of these limitation digital multimedia data need to compress. For example if there are multiple camera are connected in a network for communication then images captured by camera need to compress before communication to use proper bandwidth & for synchronized communication. Similarly local computer system has limited storage capacity & uncompressed multimedia data required high volume of storage to store. Hence multimedia data like images, videos need to be compress for many purpose. Image compression process use two technique to compress image lossless image compression & lossy image compression. Lossy Image compression needs some transformation like DCT, DFT, KLT, DST etc. Purpose of transformation is to convert the data into a form where compression is easier. This transformation will transform the pixels which are correlated into a representation where they are decorrelated. The new values are usually smaller on average than the original values. The net effect is to reduce the redundancy of representation. In Lossy image compression input image is divided in to 8*8 blocks & then each pixel is converted in to its equivalent frequency value using various transformation like DCT, DST etc. The present paper deals with the study of transformation of an 8 bit (b/w) image into its frequency domain through Discrete Sine Transform.

Data Compression Scheme Based on Discrete Sine Transform and Lloyd-Max Quantization

Abstract: With the increase of mobile equipment and transmission data, Common Public Radio Interface (CPRI) between Building Base band Unit (BBU) and Remote Radio Unit (RRU) suffers amounts of increasing transmission data. It is essential to compress the data in CPRI if more data should be transferred without congestion under the premise of restriction of fiber consumption. A data compression scheme based on Discrete Sine Transform (DST) and Lloyd-Max quantization is proposed in distributed Base Station (BS) architecture. The time-domain samples are transformed by DST according to the characteristics of Orthogonal Frequency Division Multiplexing (OFDM) baseband signals, and then the coefficients after transformation are quantified by the Lloyd-Max quantizer. The simulation results show that the proposed scheme can work at various Compression Ratios (CRs) while the values of Error Vector Magnitude (EVM) are better than the limits in 3GPP.

Discrete Fourier Transforms

Abstract: This chapter deals with the discrete Fourier transform (DFT). In Sect. 3.1, we show that numerical realizations of Fourier methods, such as the computation of Fourier coefficients, Fourier transforms or trigonometric interpolation, lead to the DFT. We also present barycentric formulas for interpolating trigonometric polynomials. In Sect. 3.2, we study the basic properties of the Fourier matrix and of the DFT. In particular, we consider the eigenvalues of the Fourier matrix with their multiplicities. Further, we present the intimate relations between cyclic convolutions and the DFT. In Sect. 3.3, we show that cyclic convolutions and circulant matrices are closely related and that circulant matrices can be diagonalized by the Fourier matrix. Section 3.4 presents the properties of Kronecker products and stride permutations, which we will need later in Chap. 5 for the factorization of a Fourier matrix. We show that block circulant matrices can be diagonalized by Kronecker products of Fourier matrices. Finally, Sect. 3.5 addresses real versions of the DFT, such as the discrete cosine transform (DCT) and the discrete sine transform (DST). These linear transforms are generated by orthogonal matrices.

Block-based interpolation filter in video coding

Abstract: In high-efficiency video coding (HEVC), fractional pixel motion compensation uses an 8-point filter and a 7-point filter, based on the discrete cosine transform (DCT), for the 1/2-pixel and 1/4-pixel interpolations, respectively. In this paper, discrete sine transform (DST)-based interpolation filters (DST-IFs) and DCT-based interpolation filters (DCT-IFs) are proposed for fractional pixel motion compensation. The DCT-IFs and DST-IFs are applied to the block, coding tree unit (CTU), to decide between DCT-IFs and DST-IFs in terms of rate-distortion optimization (RDO) process. The block-based interpolation filter method showed average Bjentegaard Delta (BD)-rate reductions of 0.8% and 0.7% in the random access (RA) and low delay B (LDB) configurations, respectively, in HEVC, whereas BD-rate is increased 0.6% in the low delay P (LDP) configuration.

Method and device for encoding/decoding images and computer readable medium

Abstract: A video decoding method, a video encoding method, and a computer readable medium are disclosed. The video decoding method includes: obtaining a prediction sample of a current block by performing intraprediction on a current block based on an intra prediction mode of a current block; parsing first information indicating whether a residual signal exists in the current block; the first information indicates that when there is a residual signal in the current block, the residual signal of the current block is acquired based on a scan direction of the residual signal for the current block; acquiring second information indicating whether to apply an inverse transform to the current block; the second information indicates that when performing inverse transform on the current block determining atransform type of the current block as a discrete cosine transform DCT or a discrete sine transform DST; obtaining an inverse transform on the residual signal of the current block based on the determined transform type of residual samples of the current block; and reconstructing the current block using the residual samples and prediction samples, the transformation type being determined independently of the intra prediction mode of the current block.

A Power efficient DST-based multicarrier and multiple access systems for VLC

Abstract: Visible Light Communication (VLC) exploits cost-effective light emitting diodes (LEDs) to render ‘illumination’ and ‘communication’ contemporaneously and is envisioned to meet the unprecedented growth in mobile data traffic. However, the slow transient response of white phosphorescent LEDs limits the modulation bandwidth. Consequently, orthogonal frequency division multiplexing (OFDM) is utilized to impart high data rate communication at the expense of emergence of high peak to average power ratio (PAPR). Furthermore, the limited dynamic range of LEDs makes this issue more pronounced as it leads to the emergence of detrimental non-linear distortions. This paper proposes discrete sine transform (DST)-based spreading for DC biased optical OFDM (DST-S-DCO-OFDM) to reduce PAPR. Unlike discrete Fourier transform (DFT)-based DCO-OFDM, DST-based DCO-OFDM doesn’t require Hermitian symmetry criteria to attain a real signal transmission. Accordingly, there is a reduction in computational complexity as well as increase in spectral efficiency. In addition, single carrier frequency division multiple access (SC-FDMA) is expedited for reducing PAPR. Therefore, this work derives the analytical expressions for DST-based optical interleaved multiple access (DST-OFDMA) and optical localized frequency division multiple access (DST-OLFDMA). The simulation results evidences that PAPR is decreased drastically by enforcing spreading technique when compared with conventional DST-based DCO-OFDM system. Furthermore, as depicted by the simulation results, the reduction in PAPR is more significant in DST-OFDMA than DST-OLFDMA. However, DST-OFDMA and DST-OLFDMA outperforms DST-based optical orthogonal frequency division multiple access (DST-OOFDMA).

Method for decoding video signal

Abstract: The invention relates to a method for decoding a video signal. The method comprises the steps of obtaining prediction mode information of a current block, the prediction mode information specifies whether the current block is an inter-frame coding block or an intra-frame coding block; in response to the current block being an intra-coded block, deriving the intra-frame prediction mode of the current block; based on the intra-frame prediction mode, generating a prediction block of the current block; based on the intra-frame prediction mode of the current block, determining the scanning type ofthe current block; obtaining the conversion coefficient of the current block based on the scanning type of the current block; and determining whether the transform type of the current block is DCT (discrete cosine transform) or DST (discrete sine transform); performing inverse transformation on the transformation coefficient based on the transformation type, so as to obtain a residual block of thecurrent block; and adding the residual block of the current block with the prediction block of the current block, to generate a reconstructed block of the current block, wherein the transform type isdetermined independently of the intra-frame prediction mode.

Perfect Reconstruction Cosine/Sine-Modulated Filter Banks in the Dolby Digital (Plus) AC-3 Audio Coding Standards

Abstract: The Dolby Digital (AC-3) and the Dolby Digital Plus or Enhanced AC-3 (E-AC-3) audio coding standards developed by the Dolby Laboratories are currently the key enabling technologies for high-quality compression of digital audio signals. For the time/frequency transformation of an audio data block, and vice versa, the AC-3 and E-AC-3 have adopted the modified discrete cosine transform (MDCT) as a perfect reconstruction cosine-modulated filter bank. The AC-3 besides the MDCT defines additional two variants of cosine-modulated filter banks called the first and second short transforms. Moreover, the current AC-3 and E-AC-3 codecs for better spectral estimation and for phase angle adjustment have adopted the modified discrete sine transform (MDST) which together with the MDCT forms a complex filter bank. This chapter is devoted to the perfect reconstruction cosine/sine-modulated filter banks used in the Dolby AC-3 and E-AC-3 audio coding standards. The chapter presents: Definitions of the analysis/synthesis AC-3 filter banks, their general symmetry properties both in the time and frequency domains, and their efficient unified implementations. Matrix representations of AC-3 filter banks, [54] their properties and relations among transform (sub-)matrices provide the basis to derive relations between the frequency coefficients and the time domain aliasing data sequences of AC-3 transforms, and in particular, the basis for derivation of a fast algorithm for conversion of frequency coefficients of AC-3 transforms directly in the frequency domain. Finally, conversion methods of the MDCT to MDST frequency coefficients directly in the frequency domain are presented.

Zero tail unique word discrete sine transform spread OFDM

Abstract: In this paper, it is proposed a new unique word (UW) OFDM waveform based on zero-tail discrete Sine transform spread OFDM (ZT UW DST-S OFDM) The proposed waveform improves the ZT DST-S-OFDM and UW OFDM methods by removing the influence of the data symbols on the tail of the transmitted signal In order to test the performance of the proposed method, computer simulation studies are performed on frequency selective Rayleigh fading channels The obtained results confirm that the proposed waveform has better peak to average power ratio (PAPR) and bit error rate (BER) performance than the conventional OFDM, ZT DFT-S OFDM and ZT UW DFT-S OFDM systems

A Prime-Factor Algorithm for the Inverse Discrete Sine Transform and its Architecture

Abstract: In this paper, we have suggested a simple scheme for prime-factor decomposition of Inverse Discrete Sine Transform (IDST) and systolic mesh architecture for its efficient implementation. In the systolic architecture the transposition of the intermediate matrix is avoided in this structure by orthogonal processing during the pair of matrix multiplication i.e., if the processing for the first matrix multiplication takes place along X-direction, the processing for the second matrix multiplication is carried out along Y-direction. Due to this feature, the systolic architecture is highly compact, offers saving for transposition hardware and at the same time yields high throughput with less latency. The proposed systolic architecture has very less area complexity, less computation time and very high VLSI performance measures compared with existing structures. Due to orthogonal nature of the Discrete Sine Transform (DST), the forward transform may however be realized by the transpositions of the inverse transform.