Transform-based Approach Research Articles

Multi-field coupling vibration patterns of the multiphase sink vortex and distortion recognition method

Fluid-induced vibration sensing technology plays an essential role in the safety and stable operation of fluid control equipment. The sensing works oriented to the multiphase sink vortex-induced vibration (MSVIV) face significant challenges in state recognition, such as the aero-engine oil pipe, metallurgical casting ladle, and microfluidic equipment. This paper presents a multi-field coupling vibration modelling and solving strategy to investigate the MSVIV transition patterns. Based on the volume of fluid and level set method, an efficient volume-correction strategy is presented to consider the mass variation and keep velocity fields without divergence. Then, a fluid–structure-acoustic dynamic model is conducted to explore multiphase vortex transport regularities. Considering the solution singularity of the fluid–solid-acoustic coupling system, a residue theorem-based solution strategy is presented to obtain the MSVIV evolution behaviors. Finally, a multichannel sensing MSVIV water-model experiment (MSVIV-WME) platform is conducted to verify the above results, and a wavelet transform-based processing approach can be utilized to obtain mutation energy features. Research results illustrate that the proposed strategy has revealed the MSVIV transition behaviors. The MSVIV process in critical states dominates nonlinear vibration patterns. The self-development sensing platform can monitor the MSVIV evolution process in real-time, and the wavelet transform-based sensing attribute with the dw3 frequency band can identify distortion characteristics. Relevant results can offer useful references for MSVIV state recognition and offer technical solving strategies for microfluidics monitoring equipment.

A multi/single-objective transform-based approach for combat task re-assignment

Cooperative combat task assignment is recently one of the hot spots in military research area, and it is generally divided by previous researchers into two separate phases, namely task pre-assignment and dynamic assignment. However, in this manner the correlation between the aforementioned two phases is to some extent neglected. This article investigates into this issue from the perspective of multi-and single-optimization, and proposes a transform method for multi/single-assignment optimization. Decision-maker's subjective preferences were obtained through their choices in the pre-assignment phase. Based on the acquired subjective preferences, the multi-objective optimization is transformed into single-objective optimization, and then the task re-assignment is completed using contract net protocol. Simulation results verify the proposed transform method as well as its applicability in dynamic assignment problems. Finally, the correlation between traditional multi-and single-objective optimization is demonstrated and a potential future research direction is outlined.

Advancing Distance Relaying Reliability: S Transform Solution for Renewable Energy-Infused Smart Grid

Distance relaying is a crucial component in safeguarding transmission lines globally. However, the presence of Sub-Synchronous Resonance (SSR) introduces challenges, as oscillations in voltage and current magnitudes adversely affect the performance of conventional distance relays. Detecting faults accurately during these oscillations poses a significant challenge for traditional relaying mechanisms. This paper addresses the issue of SSR-induced maloperations in distance relays, particularly in the context of the increasing penetration of renewable energy resources in smart grids. The integration of wind power into the grid generates sub-synchronous oscillations, leading to protection issues. In response, a novel solution leveraging the S transform, a modern signal processing technique, is proposed to enhance the robustness of distance relaying under such challenging conditions. The developed algorithm is implemented in MATLAB and rigorously tested on the First Benchmark Model of sub-synchronous resonance. Simulation of the model is conducted in the PSCAD simulation software, and the results are thoroughly validated in MATLAB. The study demonstrates the efficacy of the S transform-based approach in accurately identifying faults and mitigating maloperations caused by SSR, thereby improving the reliability of distance relaying in smart grids with high renewable energy integration.

Quasi-dynamic modeling and simulation of district heating systems: A laplace transform-based approach

The technological development direction for China's green and low-carbon energy transformation is constructing a multi-energy collaborative smart integrated energy system. As an essential subsystem of energy systems in northern China, district heating system (DHS) plays a crucial role in ensuring people's livelihood. The energy system transformation and the development of the new generation of heating systems impose increasing demands on the simulation computations of regional heating systems. This paper establishes a quasi-dynamic model for heating systems based on the Laplace transform as the foundation. It transforms the continuous thermal dynamics in the time domain into the Laplace domain for quantitatively analyzing the heat transfer loss characteristics and transmission delay characteristics in the heat transport process. Furthermore, it converts the internal complex transmission processes of the system into equivalent source-load boundary conditions to obtain a thermal state analysis model with clear physical significance. This approach significantly reduces the computational complexity of network analysis while ensuring computational accuracy. The established quasi-dynamic model is applied to cases of different scales. The computational results are compared and validated against the commercial simulation software Apros and actual operational data. The urban DHS case study calculation results show a mass flow mean relative error of 3.02% and a supply/return water temperature mean relative error of 2.46%, supporting more refined dynamic scheduling.

An empirical wavelet transform-based approach for motion artifact removal in electroencephalogram signals

Motion artifacts reduce the quality of information in the electroencephalogram (EEG) signals. In this study, we have developed an effective approach to mitigate the motion artifacts in EEG signals by using empirical wavelet transform (EWT) technique. Firstly, we decompose EEG signals into narrowband signals called intrinsic mode functions (IMFs). These IMFs are further processed to suppress the artifacts. In our first approach, principal component analysis (PCA) is employed to suppress the noise from these decomposed IMFs. In the second approach, the IMFs with noisy components are identified using the variance measure, which are then removed to obtain the artifact-suppressed EEG signal. Our experiments are conducted on a publicly available Physionet dataset of EEG signals to demonstrate the effectiveness of our approach in suppressing motion artifacts. More importantly, the IMF-variance-based approach has provided significantly better performance than the EWT-PCA based approach. Also, the IMF-variance based approach is computationally more efficient than the EWT-PCA based approach. Our proposed IMF-variance based approach achieved an average signal to noise ratio (ΔSNR) of 28.26 dB and surpassed the existing methods developed for motion artifact removal.

Gaussian Particle Filtering for Nonlinear Systems With Heavy-Tailed Noises: A Progressive Transform-Based Approach.

The Gaussian particle filter (GPF) is a type of particle filter that employs the Gaussian filter approximation as the proposal distribution. However, the linearization errors are introduced during the calculation of the proposal distribution. In this article, a progressive transform-based GPF (PT-GPF) is proposed to solve this problem. First, a progressive transformation is applied to the measurement model to circumvent the necessity of linearization in the calculation of the proposal distribution, thereby ensuring the generation of optimal Gaussian proposal distributions in sense of linear minimum mean-square error (LMMSE). Second, to mitigate the potential impact of outliers, a supplementary screening process is employed to enhance the Monte Carlo approximation of the posterior probability density function. Finally, simulations of a target tracking example demonstrate the effectiveness and superiority of the proposed method.

Semi-automated Rock Layer Recognition from Borehole Log Data Using Combined Wavelet and Fourier Transform: A Case Study in the KG basin, India

Abstract The accurate identification of rock layer interfaces from wireline logs is one of the crucial issue of geological interpretation as we face difficulties in traditional interpretations due to the presence of various kind of high and low frequencies in the log data. Determination of rock boundaries in shallow marine sediments is very important to understand several issues related to the exploration of conventional and non-conventional hydrocarbons. Presently a combined wavelet and Fourier transform-based approach was demonstrated to discriminate the rock layers from wireline log data in Krishna-Godavari basin, which were acquired during the India National Gas Hydrate Program Expedition 02 (NGHP-Exp.-02). Initially, we selected the suitable mother wavelets and optimum level of decomposition to perform the wavelet transform by computing the error between the original log signal(s) and approximation coefficients (cA’s) of the decomposed signal(s) at several decomposition levels. Subsequently, discrete wavelet transform (DWT) of a particular decomposition level was applied to the log signals to obtain the detail coefficients (cD’s), which contain the high-frequency components of the log signals. Further, these high-frequency components of the log signals were utilized in frequency spectrum-based filtering approaches. This approach was adapted to yield information about the abrupt changes occurring in the log signals across the studied depth interval. The combined application of Fourier and wavelet transforms to shallow marine log data demonstrates that this approach is an efficient tool for delineating rock layer boundaries.

A Deep Learning and Fast Wavelet Transform-Based Hybrid Approach for Denoising of PPG Signals

This letter presents a novel hybrid method that leverages deep learning to exploit the multi-resolution analysis capability of the wavelets, in order to denoise a photoplethysmography (PPG) signal. Under the proposed method, a noisy PPG sequence of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is first decomposed into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> detailed coefficients using the fast wavelet transform (FWT). Then, the clean PPG sequence is reconstructed with the help of a custom feedforward neural network (FFNN) that provides the binary weights for each of the wavelet sub-signals outputted by the inverse-FWT block. This way, all those sub-signals which correspond to noise or artefacts are discarded during reconstruction. The FFNN is trained on the Beth Israel Deaconess Medical Center (BIDMC) dataset and a custom video-PPG dataset, whereby we compute the mean squared-error (MSE) between the denoised sequence and the reference clean PPG signal, and compute the gradient of the MSE for the back-propagation. Simulation results reveal that our proposed method reduces the MSE of the PPG signal significantly (compared to the MSE of the original noisy PPG signal): by 56.40% for Gaussian noise, by 64.01% for Poisson noise, 46.02% for uniform noise, and by 72.36% for salt-and-pepper noise (with ‘db10’ mother wavelet).

Performance Investigation of Generalized Rain Pattern Absorption Attention Network for Single-Image Deraining

Rainy weather conditions are challenging issues for many computer vision applications. Rain streaks and rain patterns are two crucial environmental factors that degrade the visual appearance of high-definition images. A deep attention network-based single-image deraining algorithm is more famous for handling the image with the statistical rain pattern. However, the existing deraining network suffers from the false detection of rain patterns under heavy rain conditions and ineffective detection of directional rain streaks. In this paper, we have addressed the above issues with the following contributions. We propose a multilevel shearlet transform-based image decomposition approach to identify the rain pattern on different scales. The rain streaks in various dimensions are enhanced using a residual recurrent rain feature enhancement module. We adopt the Rain Pattern Absorption Attention Network (RaPaat-Net) to capture and eliminate the rain pattern through the four-dilation factor network. Experiments on synthetic and real-time images demonstrate that the proposed single-image attention network performs better than existing deraining approaches.

WavelNet: A novel convolutional neural network architecture for arrhythmia classification from electrocardiograms

Background and objectiveAutomated detection of arrhythmias from electrocardiograms (ECGs) can be of considerable assistance to medical professionals in providing efficient treatment for patients with cardiovascular diseases. In recent times, convolutional neural network (CNN)-based arrhythmia classification models have been introduced, but their decision-making processes remain unclear and their performances are not reproducible. This paper proposes an accurate, interpretable, and reproducible end-to-end arrhythmia classification model based on a novel CNN architecture named WavelNet, which is interpretable and optimal for dealing with ECGs. MethodsInspired by SincNet, which is capable of band-pass filtering-based spectral analysis, WavelNet was devised to achieve wavelet transform-based spectral analysis. WavelNet was trained using a subject-oriented five-class ECG arrhythmia dataset generated from the MIT-BIH Arrhythmia Database while following a benchmark scheme. By adopting various mother wavelets, multiple WavelNet-based arrhythmia classification models were implemented. To investigate whether our wavelet transform-based approach outperforms original end-to-end and band-pass filtering-based approaches, our proposed models were compared with vanilla CNN- and SincNet-based models. Model implementation and evaluation processes were repeated ten times in a Google Colab Pro+ environment. Furthermore, our most successful model was compared with state-of-the-art arrhythmia classification models for performance evaluation. ResultsThe proposed WavelNet-based models showed excellent performance on classifying non-ectopic, supraventricular ectopic, and ventricular ectopic beats because of their ability to perform adaptive spectral analysis while preserving temporal ECG information compared with vanilla CNN- and SincNet-based models. In particular, a Symlet 4 wavelet-adopting WavelNet-based model achieved the best performance with nearly 90% overall accuracy as well as the highest levels of sensitivity in classifying each arrhythmia class: 91.4%, 49.3%, and 91.4% for non-ectopic, supraventricular ectopic, and ventricular ectopic beat classifications, respectively. These results were comparable to those of state-of-the-art models. In addition, the results are reproducible, which differentiates our study from previous studies. ConclusionsOur proposed WavelNet-based arrhythmia classification model achieved remarkable performance based on a reasonable decision-making process, in comparison with other models. As its noteworthy performance is clinically reasonable and reproducible, our proposed model can contribute toward implementing a real-world precision healthcare system for patients with cardiovascular diseases.

An effective Hilbert-Huang transform-based approach for dynamic eccentricity fault diagnosis in double-rotor double-sided stator structure axial flux permanent magnet generator under various load and speed conditions

Eccentricity fault in double-sided axial flux permanent magnet generator is very difficult to be detected as the fault generated variations in terminal electrical parameters are very weak and chaotic, especially at the initial stages of the fault occurrence. In addition, one of the most important problems in any fault diagnosis approach is the investigation of load and speed variation on the proposed indices. To overcome the aforementioned difficulty and problems, this paper adopts a novelty detection algorithm based on Hilbert-Huang transform (HHT) which is a time-frequency signal analysis approach based on empirical mode decomposition and the Hilbert transform. It is well suited for reliable fault diagnosis since it is unaffected by transient conditions which make the diagnosis process incur into false alarms. The HHT-based methods has been demonstrated in recent years for rotor and bearing faults detection of induction machine and also for stator faults identification in PM synchronous machines with radial flux structure. This study explores the possibility of applying the technique to the detection of dynamic eccentricity faults in double-rotor double-sided stator structure axial flux permanent magnet generator under variable load and speed conditions. This approach relies on two steps: estimating the intrinsic mode functions (IMFs) by the empirical mode decomposition (EMD) and computing the instantaneous amplitude (IA) and instantaneous frequency (IF) of IMFs using the Hilbert transform. The more significant IMFs are determined by means of Hilbert spectrum, which is applied for accurate eccentricity fault diagnosis. The eccentricity severity can be evaluated based on the IMFs energy value. The theoretical basis of the proposed method is presented. The effectiveness of the proposed method is verified by a series of simulation and experimental tests under different conditions. The results show that the presented approach in this paper is robust against load and speed variations.

REVIEW IN IMAGES ENHANCEMENT MEDICAL USING CURVELET TRANSFORM AND VECTOR INFORMATION

The use of medical imaging for the purposes of medical monitoring and diagnosis has seen tremendous growth in recent years, which has resulted in a rising need for suitable data storage and accessibility. The primary goal of image enhancement is to generate a processed image that is suitable for a specific application. This can be accomplished by acquiring the image in the highest resolution possible or by using a variety of techniques to extract the important information while ignoring the irrelevant information. Image processing can then be performed on the processed image. Image enhancement techniques are used in medical imaging to increase the quality of the visual representation of an image by reducing the amount of noise present and sharpening the features. This study examines the Curvelet transform-based approach for increasing medical image quality. The contribution of the proposed review two steps are advised for optimizing the images. The first step is the optimization step utilizing the Curvelet transform, which featured a series of image-preparation processors. Curvelet's ability to extract complete spectrum information from an image with varying edge orientations makes it valuable for assessing data about wave propagation. In light of this, the curvelet transform is considered an excellent filter for improving and denoising images, and it is intended to deal with components in several orientations and scales. The primary objective of this treatment is to boost visibility and eliminate noise, which is superior to conventional techniques of enhancement in which the enhancement step is performed by discrete curvelet transform through wrapping. The contribution of the proposed review the usual vector is the second step of this review approach. The vector image is distributed randomly to each pixel in images that are unclear and noisy. This procedure eliminates the unpredictability in the previously computed directions and makes them regular, producing more precise results and enhancing image clarity, particularly at the image's edges. By comparing the results of the proposed technique of improvement to the results of existing improvement methods, it was determined that the proposed approach yields superior performance and is more efficient. The efficiency and efficacy of the suggested technique may be determined based on the results of the trials, which demonstrated that the method performs very well and yields accurate and precise results.

Discrete Wavelet Transform-based Approach of Real-time Wave Filtering for Dynamic Positioning of Marine Vessels

The ongoing development of deep-sea resources has contributed toward the widespread use of dynamic positioning (DP) systems that can operate in arbitrary sea areas without the limitation of operating water depth compared to mooring systems. The second-order slowly varying forces can be compensated by DP feedback control. Wave filtering techniques are crucial for designing the DP controller, which can improve the positioning performance and service of multiple actuators. The objective of wave filtering is to separate the motion induced by the first-order high-frequency oscillatory waves from the motion caused by the second-order low-frequency (LF) slowly varying disturbances. This paper proposes a novel real-time wave filtering approach for DP systems on the basis of the discrete wavelet transform without relying on the previous knowledge of dynamics of the vessel. Meanwhile, to suppress the end effects of wavelet filtering and achieve real-time application, symmetric boundary extension and the sliding window method are investigated in order to capture the slow time-varying LF motion of DP vessels. The proposed real-time wavelet filtering approach can significantly improve the quality of the separated components by selecting the optimal decomposition level, wavelet function parameters, and threshold denoising method. The real-time and filtering performance of the proposed approach is verified using a scaled model of an offshore supply vessel as well as full-scale experiments on the EXPLOERE I scientific investigation vessel under the action of winds, currents, and waves. The experimental results confirm that the proposed wave filtering algorithm is efficient and that the LF component waveform can be effectively recovered after wavelet filtering.

A correction procedure for self-induced velocity of a finite-sized particle in two-way coupled Euler–Lagrange simulations

The importance of incorporating a correction to undo the self-induced perturbation velocity of a particle, when its size becomes comparable to the Eulerian grid, in a two-way coupled Euler–Lagrange (EL) simulation is now well appreciated. The present work improves upon the prior correction procedures in a few important ways. First, the past correction procedures have been scalar-based with the assumption that the quasi-steady force is the source of self-induced velocity perturbation. Here we generalize to a vector correction procedure and thereby the directions of feedback force and relative velocity can be different. This allows the correction procedure to be used even in the presence of added-mass, history, and lift forces. Second, the effect of a nearby wall has been systematically included in the correction procedure. The correction procedure depends on fundamental Oseen solutions of streamwise and transverse regularized feedback forces. We present a Fourier transform-based analytical approach to obtaining these regularized Oseen solutions. We also present a step-by-step numerical procedure for obtaining the Oseen solutions in any EL code. With the analytical or numerical Oseen functions, the correction procedure can be easily implemented in any EL code. Iterations are required in solving the implicit correction equations and it is demonstrated that the correction procedure converges rapidly within three or four iterations. A simple empirical approach is also presented to account for unsteady effects in the correction procedure.

A Novel Method for Real Time Protection of DC Microgrid Using Cumulative Summation and Wavelet Transform

DC microgrid is a compact framework comprising interconnected nearby sources and loads. The renewable energy source used in DC microgrids being intermittent leads to the change in the power availability as well as the fault current levels. In such situations, detecting and clearing the faults is very important to protect the DC microgrid without compromising on fault clearing time and interruption of the load. This paper proposes a hybrid Cumulative Sum (CumSum) and Wavelet transform-based approach to detect the fault. The CumSum value raises the amplitude by averaging the fault current. Wavelet transforms obtain important fault current features by decomposing the current signal. The hybrid method of CumSum and Wavelet analysis proposed here enables the detection of the fault and differentiates the fault condition from sudden load variation. Additionally, it helps to recognize the location of the fault by the wavelet energy difference. The proposed scheme is tested with a developed ring-type low voltage DC (LVDC) microgrid hardware model under various fault conditions. The scheme is implemented using TMS320F28069 digital signal processors (DSP) of Texas Instruments. The hardware results are validated using MATLAB simulation. The proposed method performance is also compared with the existing methods used for DC microgrid protection. The outcome shows that the proposed method has a high accuracy of 98.72%, selectivity of 96.08%, and reliability of 99.01%. The execution time required by the proposed method is also less.

Hand-Drawn Electrical Circuit Recognition Using Object Detection and Node Recognition

With the recent developments in neural networks, there has been a resurgence in algorithms for the automatic generation of simulation ready electronic circuits from hand-drawn circuits. However, most of the approaches in the literature were confined to classify different types of electrical components. Only a few of those methods have shown a way to rebuild the circuit schematic from the scanned image, which is extremely important for further automation of netlist generation. This paper proposes (1) a real-time algorithm for the automatic recognition of hand-drawn electronic circuits and (2) subsequently rebuild the circuit schematic based on object detection and circuit node recognition. The automatic recognition employs light weight and popular you only look once version 5 (YOLOv5) for detection of circuit components and a novel Hough transform-based approach for node recognition. Using YOLOv5 object detection algorithm, a mean average precision (mAP0.5) of 98.2% is achieved in detecting the components. The proposed method is also able to rebuild the circuit schematic with 80% accuracy with a near-real-time performance of 0.33 s per schematic generation.

Implications of gnomonic distortion on electron backscatter diffraction and transmission Kikuchi diffraction.

The effect of gnomonic distortion on orientation indexing of electron backscatter diffraction patterns is explored through simulation of electron diffraction patterns for sample-to-detector geometries associated with transmission Kikuchi diffraction (TKD) and electron backscatter diffraction (EBSD). Simulated data were analysed by computing a similarity index for both Hough transformed data and simulated patterns to determine the sensitivity of each method for detecting subtle differences in the effect of gnomonic distortions on electron diffraction patterns. These results indicate that the increased gnomonic distortions in electron diffraction patterns for a TKD geometry enhance the sensitivity for detecting subtle differences in interband angles. Additionally, the utilisation of a Hough transform-based indexing approach further enhances the sensitivity.

User Rate Optimization for Fronthaul-Constrained Cell-Free Massive MIMO-OFDM Systems: A Quadratic Transform-Based Approach

As a promising candidate for the future generations of mobile communication networks, the cell-free (CF) massive multiple-input multiple-output (mMIMO) networks have been shown to provide high spectral efficiency (SE) and more uniform signal coverage than cellular mMIMO networks, enabling smart cities more diverse application services. The fronthaul link in such networks, defined as the transmission link between the central processing unit and the access point, requires a high capacity, but is often constrained. Hence, the optimization of the user rate under the limited capacity of fronthaul is the key problem to be solved in a CF networks. In this paper, we consider the downlink transmission of CF mMIMO orthogonal frequency division multiplexing (OFDM) systems with constrained transmit power and fronthaul capacity. Based on the min-max and sum-max principles, quadratic transform-min max (QT-MM) and quadratic transform-sum max (QT-SM) optimization algorithms are proposed, respectively. Simulation results show that compared with the weighted minimum mean square error (WMMSE) algorithm, both of the proposed algorithms can effectively prevent very low user rates when the fronthaul capacity is limited. When the fronthaul link capacity constraint is high, the QT-SM algorithm has better rate performance than the distributed WMMSE-d algorithm and the centralized WMMSE-c algorithm.

Melanoma Skin Cancer Detection Using Wavelet Transform and Local Ternary Pattern

Melanoma is the most serious form of skin cancer that affects millions of people globally. Through image analytics, early identification of skin cancer is enabled, resulting in more effective treatment and a lower mortality rate. The ph2 and human against machine datasets were used to collect images. After preprocessing the image with a weighted median filter, segmentation is investigated using a number of common techniques, with the best result generated by combining watershed transform and maximum similarity region merging. U-net architecture is explored for segmentation. Segmentation efficiency is calculated by dice loss and Jaccard coefficient. Segmentation architecture outperform the conventional method. Additionally, a novel wavelet transform-based approach is used to extract features, followed by local ternary pattern analysis. The intersection of the histograms, the Bhattacharya distance, the Chi-square distance, and the Pearson correlation coefficients are all computed. This inquiry makes use of only the Histogram intersection and Chi-square distance characteristics. Additional categorization is examined through the use of a range of machine learning algorithms, including the k-nearest neighbour approach, Bayesian classification, decision trees, and Support Vector Machines (SVM). When a Radial Basis Function (RBF) kernel based SVM is applied, the classification accuracy is maximised. This work is entirely devoted to binary categorization. As evidenced by the data, they outperform other state-of-the-art approaches reported in the literature. SVM classifies data with an accuracy of 98.6 percent. Weighted median filter, Watershed transform, Merging regions with the highest degree of similarity, Wavelet transform, Local Ternary Pattern, Histogram intersection Pearson correlation coefficient, chi-square distance Distance between Bhattacharya and support vector machine.

Speed enhancement of dynamic spectroscopic ellipsometry by using direct spectral phase extraction method

A rapid direct spectroscopic ellipsometric parameter extraction algorithm for computational speed enhancement of dynamic spectroscopic ellipsometry is described. The proposed direct spectral phase calculation method can provide a faster spectral phase extraction capability than a Fourier transform-based approach, while maintaining the same level of accuracy as that based on the Fourier transform method. We analyze some additional benefits and limitations of the proposed direct computational method in terms of enlarged Δ(λ) measurement spectral range and precision optimization.