scispace - formally typeset
Search or ask a question

Showing papers on "Discrete sine transform published in 2021"


Journal ArticleDOI
TL;DR: This article proposes a non-deep learning approach that searches over a set of well-known image transforms such as Discrete Wavelet Transform and Discrete Sine Transform, and classifies the features with a support vector machine-based classifier, efficiently generalizes across databases as well as different unseen attacks and combinations of both.
Abstract: Deep learning algorithms provide state-of-the-art results on a multitude of applications. However, it is also well established that they are highly vulnerable to adversarial perturbations. It is often believed that the solution to this vulnerability of deep learning systems must come from deep networks only. Contrary to this common understanding, in this article, we propose a non-deep learning approach that searches over a set of well-known image transforms such as Discrete Wavelet Transform and Discrete Sine Transform, and classifying the features with a support vector machine-based classifier. Existing deep networks-based defense have been proven ineffective against sophisticated adversaries, whereas image transformation-based solution makes a strong defense because of the non-differential nature, multiscale, and orientation filtering. The proposed approach, which combines the outputs of two transforms, efficiently generalizes across databases as well as different unseen attacks and combinations of both (i.e., cross-database and unseen noise generation CNN model). The proposed algorithm is evaluated on large scale databases, including object database (validation set of ImageNet) and face recognition (MBGC) database. The proposed detection algorithm yields at-least 84.2% and 80.1% detection accuracy under seen and unseen database test settings, respectively. Besides, we also show how the impact of the adversarial perturbation can be neutralized using a wavelet decomposition-based filtering method of denoising. The mitigation results with different perturbation methods on several image databases demonstrate the effectiveness of the proposed method.

35 citations


Journal ArticleDOI
TL;DR: The unconditional stability and sharp H 1 -norm error estimate reflecting the regularity of solution are established rigorously by the discrete energy approach.
Abstract: In consideration of the initial singularity of the solution, a temporally second-order fast compact difference scheme with unequal time-steps is presented and analyzed for simulating the subdiffusion problems in several spatial dimensions. On the basis of sum-of-exponentials technique, a fast Alikhanov formula is derived on general nonuniform meshes to approximate the Caputo’s time derivative. Meanwhile, the spatial derivatives are approximated by the fourth-order compact difference operator, which can be implemented by a fast discrete sine transform via the FFT algorithm. So the proposed algorithm is computationally efficient with the computational cost about $O(MN\log M\log N)$ and the storage requirement $O(M\log N)$ , where M and N are the total numbers of grids in space and time, respectively. With the aids of discrete fractional Gronwall inequality and global consistency analysis, the unconditional stability and sharp H1-norm error estimate reflecting the regularity of solution are established rigorously by the discrete energy approach. Three numerical experiments are included to confirm the sharpness of our analysis and the effectiveness of our fast algorithm.

15 citations


Journal ArticleDOI
TL;DR: A very efficient, unified VLSI architecture for type IV DCT/DST can be obtained, which allows the computation of the two algorithms on the same hardware, allowing an efficient incorporation of the obfuscation technique with very low overheads.
Abstract: This paper aims at solving one challenging problem in designing VLSI chips, namely, the security of the hardware, by presenting a new design approach that incorporates the obfuscation technique in the VLSI implementation of some important DSP algorithms. The proposed method introduces a new approach in obtaining a unified VLSI architecture for computing type IV discrete cosine transform (DCT-IV) and type IV discrete sine transform (DST-IV), with an efficient integration of the obfuscation technique, while maintaining low overheads. The algorithms for these two transforms were restructured in such a way that their structures are fairly similar, and thus they can be implemented on the same VLSI chip and on the same hardware with very few modifications, with the latter being attributed to the pre-processing and post-processing stages. The design proposed uses the regular and modular structures, which are named quasi-correlation, and the architecture is inspired by the paradigm of the systolic array architecture. Thus, the introduced design benefits the security, for the hardware, and also the advantages introduced by the use of the regular and modular structures. A very efficient, unified VLSI architecture for type IV DCT/DST can be obtained, which allows the computation of the two algorithms on the same hardware, allowing an efficient incorporation of the obfuscation technique with very low overheads, and it can be very efficiently implemented, offering high-speed performances and low hardware complexity, with the latter being attributed to the efficient use of the hardware resources for the computation of these two algorithms.

8 citations


Journal ArticleDOI
TL;DR: In this article, a hybrid technique called discrete sine transform (DST) is proposed for video steganography, where the least significant bits (LSBs) of the integer part of DST components are used to conceal the secret data.
Abstract: The proposed research work is presenting a novel approach in the field of steganography, especially in the compressed video domain with optimum imperceptibility to secure the secret information. In this approach, the specific secret cover video frames are selected from the sequence of video frame from which the non-dynamic region is separated. Discrete sine transform (DST) transforms this non-dynamic region from spatial domain to frequency domain. The least significant bits (LSBs) of the integer part of DST components are used to conceal the secret data. The H.264 codec is used to construct the compressed stego video using intra-frame, inter-frame prediction, motion vector estimation, transform coefficient, i.e., Discrete Cosine Transform (DCT), quantization, and entropy coding. The efficiency of the proposed hybrid technique “DST- Secret Bit Positions of Non-dynamic Region for Message (DST-SBPNRM)” for video steganography is measured by evaluating imperceptibility, robustness and embedding capacity. Moreover, the proposed technique is experimented on the well-defined video dataset and the obtained results are compared with the related work to validate the significance of the proposed work.

8 citations


Journal ArticleDOI
01 May 2021
TL;DR: A new method which uses a sixth-order compact finite difference scheme and a discrete sine transform to solve Poisson equations with Dirichlet boundary conditions and provides solutions that are in excellent agreement with the exact solution is designed.
Abstract: Compact finite difference methods are very popular for solving differential equations that arise in a wide variety of real-world applications. Despite their popularity, the efficiency of these methods is limited by the need for matrix inversion which is troubling when the size of the matrix is very large. However, there is a growing demand for methods with better accuracy and computational speed. To meet such needs, we design a new method which uses a sixth-order compact finite difference scheme and a discrete sine transform to solve Poisson equations with Dirichlet boundary conditions. The scheme is developed using the concept of higher-order Taylor series expansion which is then used to discretize Poisson equations that results in a system of linear algebraic equations. To solve this system, we propose a discrete sine transform designed based on the developed compact finite difference scheme. We proved analytically and numerically that the order of convergence of the proposed method is six. The efficiency of the new scheme is demonstrated by solving different test problems. The numerical results indicate that the proposed method outperforms an existing fourth-order scheme and provides solutions that are in excellent agreement with the exact solution.

5 citations


Journal ArticleDOI
TL;DR: A novel FOFDM method is proposed which uses inverse discrete sine and discreteSine transform (IDST/DST) and IDCT/DCT pairs together and provides the use of single-tap equalizer with the advantage of lower peak to average power ratio (PAPR).
Abstract: Intensity modulation and direct detection (IM/DD) method is widely used in optical communications. IM/DD systems require the transmitted symbols to be real-valued. Fast orthogonal frequency division multiplexing (FOFDM) is a multi-carrier communication method which can transmit by all the subcarriers and produce real-valued samples at the output. Besides the advantages of FOFDM the single-tap equalizer is unfeasible to compensate for inter symbol interference because of linear convolution property cannot be fulfilled by the inverse discrete cosine and discrete cosine transform (IDCT/DCT) pair that extensively used in FOFDM systems. In this letter, a novel FOFDM method is proposed which uses inverse discrete sine and discrete sine transform (IDST/DST) and IDCT/DCT pairs together. The proposed method provides the use of single-tap equalizer with the advantage of lower peak to average power ratio (PAPR).

5 citations


Journal ArticleDOI
30 Nov 2021-Energies
TL;DR: In this paper, fixed and adaptive supervised dictionary learning (SDL) is proposed for wide-area stability assessment, where single and hybrid fixed structures are developed based on impulse dictionary (ID), discrete Haar transform (DHT), discrete cosine transform(DCT), discrete sine transform, DST, and discrete wavelet transform for sparse features extraction and online transient stability prediction.
Abstract: Fixed and adaptive supervised dictionary learning (SDL) is proposed in this paper for wide-area stability assessment. Single and hybrid fixed structures are developed based on impulse dictionary (ID), discrete Haar transform (DHT), discrete cosine transform (DCT), discrete sine transform (DST), and discrete wavelet transform (DWT) for sparse features extraction and online transient stability prediction. The fixed structures performance is compared with that obtained from transient K-singular value decomposition (TK-SVD) implemented while adding a stability status term to the optimization problem. Stable and unstable dictionary learning are designed based on datasets recorded by simulating thousands of contingencies with varying faults, load, and generator switching on the IEEE 68-bus test system. This separate supervised learning of stable and unstable scenarios allows determining root mean square error (RMSE), useful for online stability status assessment of new scenarios. With respect to the RMSE performance metric in signal reconstruction-based stability prediction, the present analysis demonstrates that [DWT], [DHT|DWT] and [DST|DHT|DCT] are better stability descriptors compared to K-SVD, [DHT], [DCT], [DCT|DWT], [DHT|DCT], [ID|DCT|DST], and [DWT|DHT|DCT] on test datasets. However, the K-SVD approach is faster to execute in both off-line training and real-time playback while yielding satisfactory accuracy in transient stability prediction (i.e., 7.5-cycles decision window after fault-clearing).

4 citations


Journal ArticleDOI
TL;DR: The efficiency of proposed video steganography method is evaluated by performance evaluation parameters; imperceptibility, robustness, and embedding capacity and the improved results of proposed method have been compared with reported methodologies.
Abstract: The proposed research work presents a comparative analysis of Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) based video steganography in compressed domain. In this method, the random numbered secret frames are selected from the sequence of RGB cover video. This method increases the complexity level of video steganography by considering the specific host to conceal secret data. It extracts the specific non-dynamic region from secret frame, transforms the pixel value of non-dynamic region into frequency domain using transform coefficient DCT or DST. The random Least Significant Bit (LSB) of integer component of DCT and DST is used as a carrier object that leads to good video quality and secret data-carrying capacity. Furthermore, the secure compressed stego video is reconstructed by using H.264 video compression technique facilitates communication over the network channel between sender and receiver. The proposed method has been experimented on some well-known video datasets by considering RGB images with different resolutions as a secret message. The efficiency of proposed video steganography method is evaluated by performance evaluation parameters; imperceptibility, robustness, and embedding capacity and the improved results of proposed method have been compared with reported methodologies.

4 citations


Journal ArticleDOI
01 Jan 2021
TL;DR: In this article, an efficient Crank-Nicolson compact difference scheme based on the modified L1 method was proposed for solving time-fractional mobile/immobile transport equation.
Abstract: In this paper, we consider the efficient numerical scheme for solving time-fractional mobile/immobile transport equation. By utilizing the compact difference operator to approximate the Laplacian, we develop an efficient Crank-Nicolson compact difference scheme based on the modified L1 method. It is proved that the proposed scheme is stable with the accuracy of $ O(\tau^{2-\alpha}+h^4) $, where $ \tau $ and $ h $ are respectively the temporal and spatial stepsizes, and the fractional order $ \alpha\in(0, 1) $. In addition, we improve the computational performance for the non-smooth issue by the fast discrete sine transform technology and the method of adding correction terms. Finally, numerical examples are provided to verify the effectiveness of the proposed scheme.

3 citations


Journal ArticleDOI
TL;DR: A multicriteria optimization algorithm for approximate computing that aims at the identification of the optimal approximation of the DST-VII according to several approximation measures yields good performance in terms of computational complexity reduction and proximity to the exact transform while exhibiting a video coding performance comparable to the original algorithm.
Abstract: The additional discrete transforms from cosine (DCT) and sine (DST) families that come with the Adaptive Multiple Transform (AMT) approach is one of the major enhancements involved in the new Versatile Video Coding (VVC) standard. They have increasingly brought additional complexity compared to HEVC standard. The transform module is one of the most consuming stages in terms of time and hardware resources. This paper focuses on the optimization of the DST-VII transform. It deals with a multicriteria optimization algorithm for approximate computing that aims at the identification of the optimal approximation of the DST-VII according to several approximation measures. The resulting transform matrix has extremely low arithmetic complexity as well as close proximity to the exact DST-VII. Moreover, hardware synthesis results denote that the simplified design of DST-VII consumes only a third of the hardware resources used by the original algorithm. Experimental results obtained from joint exploration model simulations show a slight bit-rate increase while maintaining almost the same video quality. Such results confirm the effectiveness of the proposed approximate transform. The latter yields good performance in terms of computational complexity reduction and proximity to the exact transform while exhibiting a video coding performance comparable to the original algorithm.

2 citations


Journal ArticleDOI
TL;DR: In this article, a blind signal separation algorithm is applied on the discrete cosine transform, the discrete sine transform or the discrete wavelet transform of the mixed signals, instead of performing the separation on the mixtures in the time domain.
Abstract: Generally, most blind signal separation algorithms deal with the separation problem in the absence of noise. The presence of noise degrades the performance of separated signals. This paper deals with the problem of blind separation of audio signals from noisy mixtures. Blind signal separation algorithm is applied on the discrete cosine transform, the discrete sine transform or the discrete wavelet transform of the mixed signals, instead of performing the separation on the mixtures in the time domain. All of these transforms have an energy compaction property, which concentrates most of the signal energy in a few coefficients in the transform domain, leaving most of the transform-domain coefficients close to zero. As a result, the separation is performed on a few coefficients in the transform domain. Another advantage of signal separation in transform domains is that the effect of noise on the signals in the transform domains is smaller than that in the time domain. The paper presents also an investigation of the rule of the speech enhancement techniques as pre- and post-processing steps for the blind signal separation process, instead of performing the separation on the mixtures in the time domain. The considered speech enhancement techniques are the spectral subtraction, the Wiener filtering, the adaptive Wiener filtering, and the wavelet denoising techniques. Both blind signal separation and noise reduction are applied within a real speaker identification system to reduce the effect of interference and noise on the system performance. The simulation results confirm the superiority of transform domain separation to time domain separation and the importance of the wavelet denoising technique, when used as a pre-processing step for noise reduction. Moreover, the speaker identification system performance is enhanced with blind signal separation and noise reduction.

Journal ArticleDOI
TL;DR: In this article, the modified L1 method and the compact difference operator with fast discrete sine transform technique were used to solve the modified anomalous subdiffusion equation in two dimensions.
Abstract: The modified anomalous subdiffusion equation plays an important role in the modeling of the processes that become less anomalous as time evolves. In this paper, we consider the efficient difference scheme for solving such time-fractional equation in two space dimensions. By using the modified L1 method and the compact difference operator with fast discrete sine transform technique, we develop a fast Crank-Nicolson compact difference scheme which is proved to be stable with the accuracy of . Here, and are the fractional orders which both range from 0 to 1, and and are, respectively, the temporal and spatial stepsizes. We also consider the method of adding correction terms to efficiently deal with the nonsmooth problems. Numerical examples are provided to verify the effectiveness of the proposed scheme.

Journal ArticleDOI
TL;DR: A matrix method for constructing a modified order-8 integer sine cosine transform type VII is proposed in this paper, which is of low multiplicative complexity and requires only integer operations.
Abstract: A matrix method for constructing a modified order-8 integer sine-cosine transform type VII is proposed Based on the method, two order-8 integer modified sine-cosine transforms type VII are constructed and algorithms for fast computing of these transforms are developed, which require only integer operations These algorithms are of low multiplicative complexity, which is 7 and 105 times less, and they require 233 and 442% less additional operations than the well-known algorithm of the discrete sine transform type VII These transforms have higher coding gain performance for quality and compression ratio compared to the well-known sine transforms Algorithms for fast computing of 2D separate directional integer cosine and modified sine-cosine type VII adaptive transforms for intra prediction with 8 × 8 chroma blocks are developed These algorithms have low multiplicative complexity, which is 66 and 165 times less than that of the well-known algorithms

Journal ArticleDOI
TL;DR: In this article, the authors presented an approach for speech watermarking based on empirical mode decomposition (EMD) in different transform domains and singular value decomposition(SVD) for speaker identification.
Abstract: Biometric template protection of speech signals and information hiding in speech signals are two challenging issues. To resolve such limitations and increase the level of security, our objective is to build multi-level security systems based on speech signals. So, speech watermarking is used simultaneously with automatic speaker identification. The speech watermarking is performed to embed images into the speech signals that are used for speaker identification. The watermark is extracted for authentication, and then the effect of watermark removal on the performance of the speaker identification system in the presence of degradations is studied. This paper presents an approach for speech watermarking based on empirical mode decomposition (EMD) in different transform domains and singular value decomposition (SVD). The speech signal is decomposed in different transform domains with EMD to yield zero-mean components called intrinsic mode functions (IMFs). The watermark is inserted into one of these IMF components with SVD. A comparison between different transform domains for implementing the proposed watermarking scheme on different IMFs is presented. The log-likelihood ratio (LLR), correlation coefficient (Cr), signal-to-noise ratio (SNR), and spectral distortion (SD) are used as metrics for the comparison. According to the simulation results, we find that the watermark embedding in the discrete sine transform domain provides higher SNR and Cr values and lower SD and LLR values. The proposed approach is robust to different attacks.

Proceedings ArticleDOI
15 Jul 2021
TL;DR: In this article, an efficient algorithm for the VLSI implementation of the Inverse Discrete Sine Transform (IDST) based on quasi-band correlation structures is presented, which exhibits the advantages of a low arithmetic complexity that leads to reduced hardware and I/O costs and improved high-speed performance.
Abstract: This paper presents an efficient algorithm for the VLSI implementation of the Inverse Discrete Sine Transform (IDST) based on quasi-band correlation structures. The implementation uses a restructured form of the matrix-vector product from the IDST definition that is amenable to an efficient systolic array realization employing the quasi-band correlation type computational structure. The proposed algorithm exhibits the advantages of a low arithmetic complexity that leads to reduced hardware and I/O costs and improved high-speed performance.

Proceedings ArticleDOI
10 Jan 2021
TL;DR: In this article, a sparse coding scheme was proposed for HEVC-SCC, which takes advantage of the similar and repeated intra prediction residuals and targets low to mid frequency/energy blocks with a low sparsity setup.
Abstract: High Efficiency Video Coding - Screen Content Coding (HEVC-SCC) is an extension to HEVC which adds sophisticated compression methods for computer generated content. A video frame is usually split into blocks that are predicted and subtracted from the original, which leaves a residual. These blocks are transformed by integer discrete sine transform (IntDST) or integer discrete cosine transform (IntDCT), quantized, and entropy coded into a bitstream. In contrast to camera captured content, screen content contains a lot of similar and repeated blocks. The HEVC-SCC tools utilize these similarities in various ways. After these tools are executed, the remaining signals are handled by IntDST/IntDCT which is designed to code camera-captured content. Fortunately, in sparse coding, the dictionary learning process which uses these residuals adapts much better and the outcome is significantly sparser than for camera captured content. This paper proposes a sparse coding scheme which takes advantage of the similar and repeated intra prediction residuals and targets low to mid frequency/energy blocks with a low sparsity setup. We also applied an approach which splits the common test conditions (CTC) sequences into categories for training and testing purposes. It is integrated as an alternate transform where the selection between traditional transform and our proposed method is based on a rate-distortion optimization (RDO) decision. It is integrated in HEVC-SCC test model (HM) HM- 16.18+SCM-8.7. Experimental results show that the proposed method achieves a Bjontegaard rate difference (BD-rate) of up to 4.6% in an extreme computationally demanding setup for the "all intra" configuration compared with HM-16.18+SCM-8.7.

Book ChapterDOI
01 Jan 2021
TL;DR: In this paper, a new embedding and extraction algorithm for robust video watermarking in wavelet domain is proposed, which indicates that the proposed algorithm was superior to the current algorithms.
Abstract: Watermarking is an innovation that is utilized for giving the security to the multimedia/digital information and digital media copyright assurance. Late years, there are numerous scientists who had created watermarking algorithms based on LeaSe noteworthy Bit (LSB), Discrete Fourier Transform (DFT), Discrete Sine Transform (DST), Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) and Principle Component Analysis (PCA) and so on., Here, we proposed “a new embedding and extraction algorithms for robust video watermarking in wavelet domain”. In terms of consistency, the proposed algorithm indicates that the proposed algorithm was superior to the current algorithms. such as Structural Similarity Index (SSIM), CoVariance (CV) and Peak Signal To Noise Ratio (PSNR).

Patent
18 Mar 2021
TL;DR: In this article, a method for decoding a video signal based on adaptive multiple transforms (AMT) was proposed, where the AMT is a transform scheme that is based on a transform combination adaptively selected from a lot of transform combinations.
Abstract: FIELD: computing technology.SUBSTANCE: invention relates to video signal processing and in particular to technology for configuring a combination of transformations for each group of transform configuration singled out on the basis of at least one of the prediction modes, block size or block shape. Disclosed is a method for decoding a video signal based on adaptive multiple transforms (AMT). The method consists of the following steps: obtaining an AMT index from a video signal, wherein the AMT index indicates any of a plurality of transform combinations in a transform configuration group, and the transform configuration group includes Discrete Sine Transform Type 7 (DST7) and Discrete Cosine Transform Type 8 (DCT8); retrieving a transform combination corresponding to the AMT index, which consists of a horizontal transform and a vertical transform and includes at least one of DST-7 or DCT-8; performing inverse transformation on the current block based on the combination of transformations; and reconstructing the video signal by using the current inversely transformed block, wherein the AMT is a transform scheme that is based on a transform combination adaptively selected from a lot of transform combinations.EFFECT: improved efficiency and complexity of coding.13 cl, 19 dwg

Journal ArticleDOI
TL;DR: In this article, the authors presented a matrix factorization algorithm for discrete sine transform (DST) matrices of types I, II, III, and IV using a product of sparse, diagonal, bidiagonal, and scaled orthogonal matrices.
Abstract: This paper presents factorizations of each discrete sine transform (DST) matrix of types I, II, III, and IV into a product of sparse, diagonal, bidiagonal, and scaled orthogonal matrices. Based on the proposed matrix factorization formulas, reduced multiplication complexity, recursive, and radix-2 DST I-IV algorithms are presented. We will present the lowest multiplication complexity DST-IV algorithm in the literature. The paper fills a gap in the self-recursive, exact, and radix-2 DST I-IIII algorithms executed via diagonal, bidiagonal, scaled orthogonal, and simple matrix factors for any input $n=2^{t} \; (t \geq 1)$ . The paper establishes a novel relationship between DST-II and DST-IV matrices using diagonal and bidiagonal matrices. Similarly, a novel relationship between DST-I and DST-III matrices is proposed using sparse and diagonal matrices. These interweaving relationships among DST matrices enable us to bridge the existing factorizations of the DST matrices with the proposed factorization formulas. We present signal flow graphs to provide a layout for realizing the proposed algorithms in DST-based integrated circuit designs. Additionally, we describe an implementation of algorithms based on the proposed DST-II and DST-III factorizations within a double random phase encoding (DRPE) image encryption scheme.

Journal ArticleDOI
TL;DR: In this article, a second-order recursive equation between DST spectra in equidistant signal windows is derived, and two fast algorithms for computing the hopping DST based on the recursive relationship and input-pruned DST algorithm are proposed.
Abstract: Discrete sine transform (DST) is widely used in digital signal processing such as image coding, spectral analysis, feature extraction, and filtering. This is because the discrete sine transform is close to the optimal Karhunen–Loeve transform for first-order Markov stationary signals with low correlation coefficients. Short-time (hopping) discrete sine transform can be employed for time-frequency analysis and adaptive processing quasi-stationary data such as speech, biomedical, radar and communication signals. Hopping transform refers to a transform computed on the signal of a fixed-size window that slides over the signal with an integer hop step. In this paper, we first derive a second-order recursive equation between DST spectra in equidistant signal windows, and then propose two fast algorithms for computing the hopping DST based on the recursive relationship and input-pruned DST algorithm. The performance of the proposed algorithms with respect to computational costs and execution time is compared with that of conventional sliding and fast DST algorithms. The computational complexity of the developed algorithms is lower than any of the existing algorithms, resulting in significant time savings.

Proceedings ArticleDOI
26 Jul 2021
TL;DR: In this paper, the partial transmit sequence (PTS) and amplitude clipping (AC) methods are combined to solve the peak to average power ratio (PAPR) problem of multi-carrier MC communication systems.
Abstract: In this paper, it is recommended to combine the partial transmit sequence (PTS) and amplitude clipping (AC) methods as a solution to the peak to average power ratio (PAPR) problem of multi-carrier (MC) communication systems. The suggested technique is verified on zero tail discrete cosine transform spread OFDM (ZT-DCT-s OFDM), ZT discrete Fourier transform spread OFDM (ZT-DFT-s OFDM) and ZT discrete sine transform spread OFDM (ZT-DST-s OFDM) waveforms, from the next generation waveform alternative to OFDM, with classical OFDM waveform. Computer simulation studies are performed to verify the success of the recommended PTS-AC method over bit error rate (BER) and PAPR achievement benchmark. From the obtained results, it is observed that the suggested technique provides approximately 6 dB PAPR enhancement versus the original versions of the waveforms without compromising the BER performance.

Book ChapterDOI
01 Jan 2021
TL;DR: In this paper, orthogonal signal decomposition is decomposed into a sum of weighted decomposition basis functions (decomposition basis) like in Fourier series analysis, and the decomposition weights are found by orthogonality transformation of signal samples.
Abstract: In this chapter we learn about orthogonal signal decomposition into a sum of weighted orthogonal functions (decomposition basis) like in Fourier series analysis. The decomposition weights are found by orthogonal transformation of signal samples, i.e. by multiplying them by rectangular orthogonal matrix having complex-conjugated decomposition functions in its rows. There are many sets of decomposition functions. We learn about: discrete cosine transforms (DCTs), discrete sine transform (DST), discrete Fourier transform (DFT), Hartley, Haar, and Walsh–Hadamard transform, as well as optimal Karhunen-Loeve transform. Transform weights are called the signal spectrum in respect to the chosen set of functions. When only a few weight are significant, we a telling that the transformation has compact support. It is the case when basis functions very well fit to signal components. Orthogonal transformations of signal samples are perfect reversible—doing the inverse transformation of the weights one obtains the original signal samples. When we modify the weights and do the signal synthesis—a signal filtering operation is performed. In this chapter we become familiar with all these aspects of orthogonal signal transformations and their applications.

Journal ArticleDOI
TL;DR: In this article, a common sparse unified matrix concept is introduced, where any block size transform kernel matrix can be obtained after some mathematical operations, and the static memory required is only for 1648 elements instead of 8180 elements, each with 8-bit precision.
Abstract: In the standardization of versatile video coding (VVC), discrete cosine transform (DCT)-2, discrete sine transform (DST)-7, and DCT-8 are regarded as the primary transform kernels. However, DST-4 and DCT-4 can also be considered as the transform kernels instead of using DST-7 and DCT-8 owing to their effectiveness in smaller resolution test sequences. To implement these different block size transform kernels, a considerable amount of memory has to be allocated. Moreover, memory consumption to store different block size transform kernels is regarded as a major issue in video coding standardization. To address this problem, a common sparse unified matrix concept is introduced in this study, where any block size transform kernel matrix can be obtained after some mathematical operations. The proposed common sparse unified matrix saves approximately 80% of the static memory by storing only a few transform kernel elements for DCT-2, DST-7, and DCT-8. Full-required transform kernels are derived using the stored transform kernels and generated unit-element matrices and a permutation matrix. The static memory required is only for 1648 elements instead of 8180 elements, each with 8-bit precision. The defined common sparse unified matrix is composed of two parts: a unified DST-3 matrix and a grouped DST-7 matrix. The unified DST-3 matrix is used to derive different points of DCT-2 transform kernels, and the grouped DST-7 matrix is used to derive different points of DST-7 and DCT-8 transform kernels. The new technique of grouping concept is introduced, which shows the relationship between different rows of DST-7 transform kernels with various block sizes. The proposed grouping concept supports the fast algorithm of DST-7 by implementing the proposed method of the “one group one feature” principle. The simulation was conducted using the VTM-3.0 reference software under common test conditions. The simulation result of the all intra (AI) configuration is Y = 0.00%, U = −0.02%, V = 0.00% with an encoding time of 100%, and a decoding time of 100%. Similarly, the simulation results of random access (RA) configuration are Y = −0.01%, U = 0.09%, V = 0.06%, and the encoding and decoding times are 101% and 100%, respectively. The simulation result of the low delay B (LDB) configuration is Y = 0.01%, U = 0.08%, and V = −0.27%, for encoding and decoding times of 101% and 100%, respectively.

Book ChapterDOI
01 Jan 2021
TL;DR: An efficient design approach is used for implementation of discrete sine transform (DST) and based on an appropriate formulation of transform a systolic architecture is presented, well suited for VLSI implementation.
Abstract: In this paper, an efficient design approach is used for implementation of discrete sine transform (DST). A new algorithm for DST for N = 4n has been suggested and based on an appropriate formulation of transform a systolic architecture is presented. Design uses lesser hardware and outperform in terms of delay thus the architecture well suited for VLSI implementation.