Discrete Sine Transform Research Articles

A combination of DST precoder and ICF based-methods for PAPR suppression in OFDM signal

Abstract One well-known demerit of orthogonal frequency division multiplexing (OFDM) is its high peak-to-average power ratio (PAPR) which limits the efficiency of high-power amplifier (HPA) and also destroys its bit error rate (BER) performance. Hence, a method based on grouping of discrete sine transform (DST) precoder and iterative clipping and filtering (ICF) is proposed to reduce PAPR in this article. The DST precoder reduces PAPR to certain level by changing phase of the signal. Moreover, the ICF technique is also implemented in DST based-OFDM signal for additional minimization of PAPR. Therefore, the proposed method (DST-ICF) preserves BER performance also from other existing methods. At complementary cumulative distribution function (CCDF) = 10−3, the simulation results indicate the proposed technique that minimizes PAPR with iteration values (I = 1, I = 2, and I = 3) to 6.37 dB, 5.29 dB, and 4.81 dB respectively. Moreover, at same BER, the E b /N 0 of proposed technique with iteration value (I = 3) is achieved by 9.75 dB for quadrature phase shift keying (QPSK).

A novel α-absolute value preconditioner for all-at-once systems from heat equations

In this paper, we generalize a fast Fourier transforms (FFTs) based preconditioner and propose a novel α-absolute value preconditioner for all-at-once systems from heat equations. Our preconditioner is symmetric positive definite and can also be computed efficiently using fast Fourier transforms or discrete sine transforms (DSTs). Furthermore, we prove that the corresponding preconditioned matrix has a unitary-plus-low-rank decomposition, and the eigenvalues of the preconditioned matrix are clustered at ±1, which leads to fast convergence rate of the preconditioned MINRES method. Finally, numerical examples on all-at-once systems from heat equations with different discretization scheme demonstrate the effectiveness of our new preconditioner.

Application of the QDST algorithm for the Schrödinger particle simulation in the infinite potential well

This paper examines whether a quantum computer can efficiently simulate the time evolution of the Schrödinger particle in a one-dimensional infinite potential well. In order to solve the Schrödinger equation in the quantum register, an algorithm based on the Quantum Discrete Sine Transform (QDST) is applied. The paper compares the results obtained in this way with the results given by the previous method (based on the QFT algorithm).

Enhancing speaker identification through reverberation modeling and cancelable techniques using ANNs.

This paper introduces a method aiming at enhancing the efficacy of speaker identification systems within challenging acoustic environments characterized by noise and reverberation. The methodology encompasses the utilization of diverse feature extraction techniques, including Mel-Frequency Cepstral Coefficients (MFCCs) and discrete transforms, such as Discrete Cosine Transform (DCT), Discrete Sine Transform (DST), and Discrete Wavelet Transform (DWT). Additionally, an Artificial Neural Network (ANN) serves as the classifier for this method. Reverberation is modeled using varying-length comb filters, and its impact on pitch frequency estimation is explored via the Auto Correlation Function (ACF). This paper also contributes to the field of cancelable speaker identification in both open and reverberation environments. The proposed method depends on comb filtering at the feature level, deliberately distorting MFCCs. This distortion, incorporated within a cancelable framework, serves to obscure speaker identities, rendering the system resilient to potential intruders. Three systems are presented in this work; a reverberation-affected speaker identification system, a system depending on cancelable features through comb filtering, and a novel cancelable speaker identification system within reverbration environments. The findings revealed that, in both scenarios with and without reverberation effects, the DWT-based features exhibited superior performance within the speaker identification system. Conversely, within the cancelable speaker identification system, the DCT-based features represent the top-performing choice.

Secure image transmission through LTE wireless communications systems

Secure transmission of images over wireless communications systems can be done using RSA, the most known and efficient cryptographic algorithm, and OFDMA, the most preferred signal processing choice in wireless communications. This paper aims to investigate the performance of OFDMA system for wireless transmission of RSA-based encrypted images. In fact, the performance of OFDMA systems; based on different signal processing techniques, such as, discrete sine transforms (DST) and discrete cosine transforms (DCT), as well as the conventional discrete Fourier transforms (DFT) are tested for wireless transmission of gray-scale images with/without RSA encryption. The progress of transmitting the image is carried by firstly, encrypting the image with RSA algorithm. Then, the encrypted image is modulated with DFT-based, DCT-based, and DST-based OFDMA systems. After that, the modulated images are transmitted over a wireless multipath fading channel. The reverse operations will be carried at the receiver, in addition to the frequency domain equalization to overcome the channel effect. Exhaustive numbers of scenarios are performed for study and investigation of the performance of the different OFDMA systems in terms of PSNR and MSE, with different subcarriers mapping and modulation techniques, is done. Results indicate that the ability of different OFDMA systems for wireless secure transmission of images. However, the DCT-OFDMA system showed superiority over the DST-OFDMA and the conventional DFT-OFDMA systems.

The performance of DST-Wavelet feature extraction for guitar chord recognition

Small systems can be designed to be more energy-efficient compared to larger systems. On small systems, the need for data processing with small data sizes becomes a necessity. In the context of small systems for guitar chord recognition, there are indications that further efforts can be made to reduce the size of feature extraction data. This paper introduces DST (Discrete Sine Transform)-Wavelet feature extraction to achieve this reduction. Basically, this work evaluated the frame blocking length, the number of DST cutting factors, and the type of wavelet filters (Daubechies and biorthogonal families) to obtain the optimal number of feature extraction data. Based on the evaluation, the optimal result obtained was a number of four feature extraction data. This optimal result was obtained by using a frame blocking length of 512 points, a DST cutting factor of 0.5, and a biorthogonal 3.3 wavelet filter. Testing with 140 test chords using these four feature extraction data could give an accuracy of up to 92.86%.

Performance analysis of wireless compressed-image transmission over DST-based OFDMA systems

Multimedia data, like images, consumes significant bandwidth when transmitted over wireless systems. Therefore, compressing transmitted images becomes crucial to reduce the required bandwidth and improve energy efficiency. This work aims to analyze the performance of transmitting wireless compressed images over a recent Discrete Sine Transform (DST)-Based Orthogonal Frequency Division Multiple Access (DST-OFDMA) system. It investigates the effectiveness of several image compression methods by determining the minimum Signal-to-Noise Ratio (SNR) required for each method to achieve error-free image recovery at the receiver. This work considers different modulation schemes including 16QAM and QPSK, as well as different subcarrier mapping schemes (localized and interleaved) over vehicular A, SUI3, and uniform channels. Nine standard compression methods are used for analyzing the performance of the DST-OFDMA system and compared it with that of the conventional Discrete Fourier Transform (DFT)-based OFDMA (DFT-OFDMA) system. The results show that the performance of DST-OFDMA outperforms that of DFT-OFDMA, especially when QPSK modulation is used. Simulation results demonstrate that the interleaved DST-OFDMA (DST-IOFDMA) system, employing the SPIHT_3D compression method and QPSK modulation (over the SUI3 channel model), achieves the lowest SNR value required for compressed image recovery, approximately 18 dB. This indicates that the SPIHT_3D compression method exhibits lower power consumption compared to other methods as well as high bandwidth efficiency.

Evaluation of orthogonal frequency‐division multiple‐access systems in the presence of carrier frequency offset using wireless images transmission

AbstractOrthogonal Frequency‐Division Multiple‐Access (OFDMA) is used in different recent wireless communication systems. However, it is susceptible to carrier frequency offset (CFO) which effects the orthogonality between subcarriers and causes inter‐carrier interference (ICI) and multiple access interference (MAI). The aim of this paper is to analyze the impact of the CFOs on the performance of Discrete Sine Transform (DST) DST‐OFDMA, Discrete Cosine Transform (DCT) DCT‐OFDMA and Discrete Fourier Transform (DFT) DFT‐OFDMA systems and to evaluate them with different modulation schemes and different subcarriers mapping schemes over vehicular A and Stanford University Interim (SUI) 3 channels. Transmission of image over the wireless system is performed to analyze and investigate the performance in terms of the Peak Signal‐to‐Noise Ratio (PSNR), and the Mean Square Error (MSE). Through the evaluation, with CFO compensation, without CFO, and without CFO compensation cases are considered. In this work, Joint Minimum Mean Square Error (JMMSE) equalization and CFO compensation technique is used. It is noted that when the QPSK scheme and the SUI3 channel model are used then the DCT‐OFDMA system provides better MSE and PSNR performances than other systems for the JMMSE compensation technique.

ASCO-OFDM based VLC system throughput improvement using PAPR precoding reduction techniques

The huge bandwidth and immunity to electromagnetic interference make visible light communication (VLC) systems the preferred technique for many applications. Unfortunately, the superposition of multiple subcarriers in VLC orthogonal frequency division multiplexing systems leads to a high peak-to-average power ratio (PAPR). So, in this study, we aim to reduce PAPR in VLC systems and improve the system performance by proposing non-distorting PAPR reduction techniques like precoding techniques as it doesn’t affect the system data rate because they do not require any obligatory transmission of side information. Moreover, it has a very good ability to reduce the PAPR without affecting the system BER performance. So, different precoding reduction techniques are proposed like discrete cosine transform (DCT), discrete sine transform (DST), discrete Hatley transform (DHT), and Vandermonde like matrix (VLM), to address the high PAPR and light-emitting diode-restricted linear range problems in VLC systems. The proposed technique using DHT, DCT, DST, and VLM provided a significant advantage in reducing the PAPR by 1.35 dB, 1.46 dB, 2.12 dB, and 2.17 dB, respectively. So the proposed technique is based on using the VLM precoding technique to achieve maximum reachable PAPR reduction value. Also, a comparison of the presented work and related literature reviews for PAPR reduction techniques are held to ensure the validity and effectiveness of the proposed scheme.

Image Compression using All-optical DCT and DST

In this paper, we present a method for realizing all-optical Discrete Sine and Cosine Transform (DST/DCT) for image compression. We show that all-optical DST and DCT can be achieved by using only one 4x4 MMI (multimode interference) coupler at a suitable width and length. The proposed method can process image data at high speed and high bandwidth. We use numerical methods for simulating the whole devices

Impact of STO and STO-estimation in DST-DCO-OFDM-based visible light communication systems

This work addresses the timing synchronization aspects in a DC-biased optical OFDM (DCO-OFDM) system which is exploiting real trigonometric transform like discrete sine transform (DST). The striking notability is that without the necessity of Hermitian Symmetry criteria, the optical OFDM system takes the advantage of real signal processing transformation techniques like DST. Furthermore, this paper compares the performance of timing synchronization algorithms exploiting the periodicity property of the DST-DCO-OFDM symbol with the training symbol-based STO estimation algorithm. Among the STO estimation algorithms, the training symbol-based STO estimation technique imparts a better mean square error when compared with that of the periodicity-based STO estimation algorithms. Moreover, this work validates the derived Cramer Rao Lower Bound (CRLB) for the timing errors.

An Overview of Systolic Arrays for Forward and Inverse Discrete Sine Transforms and Their Exploitation in View of an Improved Approach

This paper aims to present a unified overview of the main Very Large-Scale Integration (VLSI) implementation solutions of forward and inverse discrete sine transforms using systolic arrays. The main features of the most important solutions to implement the forward and inverse discrete sine transform (DST) using systolic arrays are presented. One of the central ideas presented in the paper is to emphasize the advantages of using regular and modular systolic array computational structures such as cyclic convolution, circular correlation, and pseudo-band correlation in the VLSI implementation of these transforms. The use of such computational structures leads to architectures well adapted to the features of VLSI technologies, with an efficient use of the hardware structures and a reduced I/O cost that helps avoiding the so-called I/O bottleneck. With the techniques presented in this review, we have developed a new VLSI implementation of the DST using systolic arrays that allow efficient hardware implementation with reduced complexity while maintaining high-speed performances. Using a new restructuring input sequence, we have been able to efficiently reformulate the computation of the forward DST transform into a special computational structure using eight short quasi-cycle convolutions that can be computed with low complexity and where some of the coefficients are identical. This leads to a hardware structure with high throughput. The new restructuring sequence is the use of the input samples in a natural order as opposed to previous solutions, leading to a significant reduction of the hardware complexity in the pre-processing stage due to avoiding a permutation stage to reverse the order. Moreover, the proposed VLSI architecture allows an efficient incorporation of the obfuscation technique with very low overheads.

Denoising Marine Controlled Source Electromagnetic Data Based on Dictionary Learning

Marine controlled source electromagnetic (CSEM) is an efficient method to explore ocean resources. The amplitudes of marine CSEM signals decay rapidly with the measuring offsets. The signal is easily contaminated by various kinds of noise when the offset is large. These noise include instrument internal noise, dipole vibration noise, seawater motion noise and environmental noise Suppressing noise is the key to improve data quality and interpretation accuracy. Sparse representation based denoising method has been used for denoising for a long time. provides a new way to remove noise. Under the framework of sparse representation, the denoising effect is closely related to the chosen transform matrix. This matrix is called dictionary and its column named atom. In general, the stronger the correlation between signal and dictionary is, the sparser representation will be, and further the better the denoising effect will be. In this article, a new method based on dictionary learning is proposed for marine CSEM denoising. Firstly, the signal segments suffering little from noise are captured to compose the training set. Then the learned dictionary is trained from the training set via K-singular value decomposition (K-SVD) algorithm. Finally, the learned dictionary is used to sparsely represent the contaminated signal and reconstruct the filtered one. The effectiveness of the proposed approach is verified by a synthetic data denoising experiment, in which windowed-Fourier-transform (WFT) and wavelet-transform (WT) denoising methods and three dictionaries (discrete-sine-transform (DST) dictionary, DST-wavelet merged dictionary and the learned dictionary) under a sparse representation framework are tested. The results demonstrate the superiority of the proposed dictionary-learning-based denoising method. Finally, the proposed approach is applied to field data denoising process, coupled with DST and DST-wavelet dictionaries based denoising methods. The outcomes further proves that the propsoed approach is effective and superior for marine CSEM data denoising.

Comparison of discrete transforms for deep‐neural‐networks‐based speech enhancement

In recent studies of speech enhancement, a deep-learning model is trained to predict clean speech spectra from the known noisy spectra of speech. Rather than using the traditional discrete Fourier transform (DFT), this paper considers other well-known transforms to generate the speech spectra for deep-learning-based speech enhancement. In addition to the DFT, seven different transforms were tested: discrete Cosine transform, discrete Sine transform, discrete Haar transform, discrete Hadamard transform, discrete Tchebichef transform, discrete Krawtchouk transform, and discrete Tchebichef-Krawtchouk transform. Two deep-learning architectures were tested: convolutional neural networks (CNN) and fully connected neural networks. Experiments were performed for the NOIZEUS database, and various speech quality and intelligibility measures were adopted for performance evaluation. The quality and intelligibility scores of the enhanced speech demonstrate that discrete Sine transformation is better suited for the front-end processing with a CNN as it outperformed the DFT in this kind of application. The achieved results demonstrate that combining two or more existing transforms could improve the performance in specific conditions. The tested models suggest that we should not assume that the DFT is optimal in front-end processing with deep neural networks (DNNs). On this basis, other discrete transformations should be taken into account when designing robust DNN-based speech processing applications.

On [formula omitted] matrix-based approximate inverse preconditioning technique for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations

In this paper, we firstly explore the special structure of the discretized linear systems from the spatial fractional diffusion equations. The coefficient matrices of the resulting discretized systems have a diagonal-plus-Toeplitz structure. Because the resulting Toeplitz matrix is symmetric positive definite (SPD), then we can employ the τ matrix to approximate it. By making use of the piecewise interpolation polynomials, we propose a new approximate inverse preconditioner to handle the diagonal-plus-Toeplitz coefficient matrices. The τ matrix-based approximate inverse (TAI) preconditioning technique can be implemented very efficiently by using discrete sine transforms(DST). Theoretically, we have proved that the spectrum of the resulting preconditioned matrices are clustered around one. Thus, Krylov subspace methods with the proposed preconditioners converge very fast. To demonstrate the efficiency of the new preconditioners, numerical experiments are implemented. The numerical results show that with the proper interpolation node numbers, the performance of the τ-matrix based preconditioning technique is better than the other tested preconditioners.

Directional Analytic Discrete Cosine Frames

Block frames called <i>directional analytic discrete cosine frames</i> (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global memory access. These characteristics are strongly required for current high-resolution image processing. Specifically, we propose two DADCFs based on discrete cosine transform (DCT) and discrete sine transform (DST). The first DADCF is constructed from parallel separable transforms of DCT and DST, where the DST is permuted by row. The second DADCF is also designed based on DCT and DST, while the DST is customized to have no DC leakage property which is a desirable property for image processing. Both DADCFs have rich directional selectivity with slightly different characteristics each other and they can be implemented as non-overlapping block-based transforms, especially they form Parseval block frames with low transform redundancy. We perform experiments to evaluate our DADCFs and compare them with conventional directional block transforms in image recovery.

DCT and DST Filtering With Sparse Graph Operators

Graph filtering is a fundamental tool in graph signal processing. Polynomial graph filters (PGFs), defined as polynomials of a fundamental graph operator, can be implemented in the vertex domain, and usually have a lower complexity than frequency domain filter implementations. In this paper, we focus on the design of filters for graphs with graph Fourier transform (GFT) corresponding to a discrete trigonometric transform (DTT), i.e., one of 8 types of discrete cosine transforms (DCT) and 8 discrete sine transforms (DST). In this case, we show that multiple sparse graph operators can be identified, which allows us to propose a generalization of PGF design: multivariate polynomial graph filter (MPGF). First, for the widely used DCT-II (type-2 DCT), we characterize a set of sparse graph operators that share the DCT-II matrix as their common eigenvector matrix. This set contains the well-known connected line graph. These sparse operators can be viewed as graph filters operating in the DCT domain, which allows us to approximate any DCT graph filter by a MPGF, leading to a design with more degrees of freedom than the conventional PGF approach. Then, we extend those results to all of the 16 DTTs as well as their 2D versions, and show how their associated sets of multiple graph operators can be determined. We demonstrate experimentally that ideal low-pass and exponential DCT/DST filters can be approximated with higher accuracy with similar runtime complexity. Finally, we apply our method to transform-type selection in a video codec, AV1, where we demonstrate significant encoding time savings, with a negligible compression loss.

Secure Audio Transmission Over Wireless Uncorrelated Rayleigh Fading Channel

Audio communications and computer networking play essential roles in our daily lives, including many domains with different scopes. Developments in these technologies are quick. In consequence, there is a dire need to secure these technologies up to date. This paper presents an efficient model for secure audio signal transmission over the wireless noisy uncorrelated Rayleigh fading channel. Also, the performance of the utilized multiple secret keys-based audio cryptosystem is analyzed in different transformation domains. The discrete cosine transform (DCT), the discrete sine transform (DST), and the discrete wavelet transform (DWT) are investigated in the utilized multiple secret key-based audio cryptosystem. Simulation results show consistent results with the wireless noisy channel. The performance of the proposed multiple secret keys-based audio cryptosystem can be ranked concerning the employed domain as DWT, DCT, and DST transform techniques. The simulation experiments proved that the presented multiple secret keys-based audio cryptosystem for audio signals transmitted over the wireless noisy uncorrelated Rayleigh fading channel achieves reliable and secure wireless link utilizing combined multi security layers.

Precoded SLM and PTS Scheme for Reduced PAPR in OFDM for Wireless Communications

Orthogonal Frequency Division Multiplexing (OFDM) contribute high data rates in current as well as future wireless communication systems but it aches from high Peak to Average Power Ratio (PAPR). But this high PAPR makes the High-Power Amplifier (HPA) complex which increases the cost of it and leads to the drawbacks like Inter Carrier Interference (ICI) and rise in out of band radiation. Even though many techniques are there to decrease the complexity of HPA by reducing the PAPR, Selected Mapping (SLM) and the Partial Transmit Sequence (PTS) provides less PAPR with low complexity. In this paper, both PTS and SLM are combined with Discrete Sine Transform (DST) and their PAPR and efficiencies are also compared with OFDM signal. The proposed hybrid DST-PTS and DST-SLM provides less PAPR compared to OFDM, SLM and PTS techniques with low complexity. Also, the bit error rate for DST-SLM and DST-PTS techniques are compared for different values of SNR. In future wireless communication systems, these proposed techniques can be used as they provide less bit error rate and less PAPR with low complexity

Sparse Signal Reconstruction on Fixed and Adaptive Supervised Dictionary Learning for Transient Stability Assessment

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).