Orthogonal Filter Research Articles

Virtual torque sensor for electrical bicycles

We present a novel approach to the reconstruction of the physical pedalling torque in an electrically powered bicycle. The external force due to the road slope that is acting on the bicycle is estimated employing the reconstruction of the inclination angle with an orthogonal filter. This orthogonal filter uses an adaptive weighting between gyroscope and accelerometer sensor data. The applied weighting function is based on the bicycle’s acceleration, estimated from a bicycle velocity sensor. By employing a nonlinear physical model of the bicycle, the cyclist’s pedalling torque is reconstructed with an Unscented Kalman Filter. Experimental results from the inclination angle estimator and virtual torque sensor for different road slopes underline the performance of the proposed approach.

Efficient Orthogonal Bicomplex Bilinear DSP Algorithm Design

Abstract The present paper describes the development of a new technique for designing orthogonal bicomplex Digital Signal Processing (DSP) algorithms. In contrast to those previously reported on, this novel method is of universal application while being unaffected by either the type or the order of the real digital processing algorithm employed as a prototype. The proposed technique builds on Watanabe and Nishihara’s complex orthogonal transformation, and converts real or complex orthogonal transfer functions into bicomplex orthogonal ones. In this study, the new technique is applied to the design and testing of orthogonal bilinear bicomplex filters with a canonical number of elements, the main advantage of which is that they are several times lower in order. In this way, bilinear bicomplex orthogonal transfer functions are made up of real coefficient ones of the fourth-order, thereby reducing the order of the filter by a factor of four. The experiments demonstrate that the properties of the prototype filter are acquired by the bicomplex orthogonal filters, irrespective of the prototype being complex or real in nature.

Comparison between Orthogonal and Bi-Orthogonal Wavelets

Theoretical aspects and analysis of wavelets have applications in mathematical modeling, artificial neural networks, digital signal processing, and image processing and numerical methods. The term orthogonal deals with the mathematical part which covers a wide area of digital signal processing and image processing. An orthogonal wavelet generates the wavelet whose nature is orthogonal. This means an inverse or transpose wavelet transform is nothing but the adjoint of a wavelet transform. If this condition fails by missing orthogonality it may result in biorthogonal wavelets. Single scaling functions and single wavelets are generated but orthogonal wavelet filter bank. A biorthogonal wavelet associated with the wavelet transformation is invertible. There is no need that if it is invertible so it should be orthogonal. The biorthogonal wavelet allows maximum freedom in the case of designing the orthogonal wavelet. It also supports the construction of symmetric wavelet functions. In biorthogonal wavelets, as the name indicates, two scaling factors or functions are responsible for the generation of the various multi-resolutions on the basis of different wavelets. For the image and signal reconstruction purpose we need that wavelet. We get a better result in the presence of biorthogonal wavelets. In the present work, we analyzed the performance of orthogonal and biorthogonal wavelet filters for image processing. We test the image and observed that the filter coefficient and image quality for the orthogonal and biorthogonal wavelet. On the basis of performance analysis it is concluded that biorthogonal wavelets are better than orthogonal wavelets.

Research on NMR Noise Reduction Method Based on Improved CEEMD

Low-field NMR technology has been widely used in many fields, among which the most representative method is the use of CPMG sequence for T2 measurement. Important parameters such as permeability, saturation and fluid type of porous media can be obtained by T2 spectrum inversion calculation of NMR echo sequence signal. However, T2 spectrum inversion calculation is easily affected by noise signals. Improving the signal-to-noise ratio (SNR) of echo signal is one of the key problems with the application of low-field NMR technology. Therefore, in order to obtain more accurate analysis results, it is necessary to develop corresponding noise reduction methods. The past researches on NMR signal noise reduction mainly focus on echo string. In this paper, a complete NMR signal model is constructed, and the problem of the echo and echo string de-noising is discussed. FIR filter and orthogonal modulation filter (OMF) are studied for noise reduction of echo. To solve the problem of echo string de-noising, an improved complementary ensemble empirical mode decomposition (CEEMD) threshold de-noising method is proposed and compared with the heuristic threshold de-noising method based on sym4 wavelet and the previous empirical mode decomposition (EMD) threshold de-noising method. Based on the construction model and practical verification, it is proved that the proposed method can invert the more accurate T2 spectrum while improving the signal-to-noise ratio. The research results of this paper provide a strong support for the application of low-field NMR technology in the environment of strong noise.

Orthogonal Periodic Sequences for the Identification of Functional Link Polynomial Filters

The paper introduces a novel family of deterministic periodic signals, the orthogonal periodic sequences (OPSs), that allow the perfect identification on a finite period of any functional link polynomials (FLiP) filter with the cross-correlation method. The class of FLiP filters is very broad and includes many popular nonlinear filters, as the well-known Volterra and the Wiener nonlinear filters. The novel sequences share many properties of the perfect periodic sequences (PPSs). As the PPSs, they allow the perfect identification of FLiP filters with the cross-correlation method. But, while PPSs exist only for orthogonal FLiP filters, the OPSs allow also the identification of non-orthogonal FLiP filters, as the Volterra filters. In OPSs, the modeled system input can be any persistently exciting sequence and can also be a quantized sequence. Moreover, OPSs can often identify FLiP filters with a sequence period and a computational complexity much smaller that PPSs. The provided experimental results, involving the identification of real devices and of a benchmark model, highlight the potentialities of the proposed OPSs in modeling unknown nonlinear systems.

Mueller matrix ellipsometry study of a circular polarizing filter

The authors introduce an ellipsometric data analysis strategy for a flexible polymeric circular polarizing filter consisting of a thin linear polarizer and quarter-wave plate sandwich. The circular polarizing filter is an inhomogeneous optical system exhibiting different optical responses depending on the propagation direction of light. If light enters from the linear polarizer, the transmitted beam is linearly polarized before entering the quarter-wave plate. The orientation of the quarter-wave plate is rotated 45° from the linear polarizer axis. The emerging light from the quarter-wave plate is circularly polarized. If light is circularly polarized and enters from the reserve side, the quarter-wave plate converts it into linearly polarized light. The following linear polarizer either transmits or absorbs the beam depending on the handedness of the original circular polarization. The optical response in the forward direction is utilized in photography to reduce unwanted reflections in the image. The optical response in the reverse direction is utilized in 3D eyeglasses, which consist of two orthogonal circular polarizing filters to separate the left and right images. Mueller matrix spectroscopic ellipsometry is used to observe the optical responses of a circular polarizing filter in both directions. The authors demonstrate data analysis procedures for individual layers to find the optical constants in a wide spectral range from 400 to 1700 nm. The circular polarizing filter measured in the forward direction enables ellipsometry to determine the included angle between the linear polarizer and the quarter-wave plate. The ellipsometric data analysis result is used to predict transmitted light intensity versus rotation angle (deg) with respect to any input polarization state.

NEW CLASS OF DIGITAL MALMQUIST-TYPE ORTHOGONAL FILTERS BASED ON THE GENERALIZED INNER PRODUCT; APPLICATION TO THE MODELING DPCM SYSTEM

A new class of cascade digital orthogonal filters of the Malmquist type based on bilinear transformation for mapping poles to zeroes and vice versa is presented in this paper. In a way, it is a generalization of the majority of the classical orthogonal filters and some newly designed filters as well. These filters are orthogonal with respect to the generalized inner product which is actually a generalization of the classical inner product. Outputs of these filters are obtained by using polynomials orthogonal with respect to the new inner product. The main quality of these filters is that they are parametric adaptive. The filter with six sections is practically realized in the Laboratory for Modeling, Simulation and Control Systems. Performances of the designed filter are proved on modeling and identification of the system for differential pulse code modulation. Real response and response from the proposed filter are compared with regard to the chosen criteria function. Also, a comparative analysis of the proposed filter with some existing filters is performed.

Synthesis and Realization of Two-Dimensional Separable Denominator Orthogonal Systems via Decomposition Into 1-D Systems

This paper presents a realization and implements techniques of 2-D linear time-invariant discrete filters described by a system function. Two classes are covered: finite- and infinite-impulse response systems with a separable denominator. This realization is based on a state-space approach, known as orthogonal filters, resulting in structures consisting of Givens rotations and delays. The techniques that are presented are illustrated by an edge detection system and a separable denominator band-pass filter designs. For the designed structures, magnitude errors caused by a finite precision arithmetic have been evaluated and compared with those obtained for direct structures based on difference equations. It has been shown that orthogonal structures possess lower magnitude errors.

Automated Detection of Sleep Stages Using Energy-Localized Orthogonal Wavelet Filter Banks

Sleep is an integral part of human life which provides the body with much-needed rest which facilitates recovery and promotes health. Sleep disorders, however, lead to a reduced quality of sleep and as a result, affect the standard of human life. It is important to classify sleep stages in order to detect sleep disorders. Electroencephalogram (EEG) signals are obtained from patients under observation. But, classifying these EEG signals into various sleep stages is an arduous task. It becomes more difficult when one tries to classify EEG signals visually. Even sleep specialists struggle to classify the EEG signals into different sleep stages by visual inspection. Several approaches have been adopted by scientists across the world to mitigate these errors by using EEG and polysomnogram signals. In this paper, an automated method has been proposed for scoring various sleep stages employing EEG signals. We have employed a two-band energy-localized filter in the time-frequency domain, which decomposed six sub-bands using five-level wavelet decomposition. Subsequently, we compute discriminatory features namely fuzzy entropy and log energy from the decomposed coefficients. The extracted features are fed to various supervised machine learning classifiers. Our proposed approach yielded an accuracy of 91.5% and 88.5% for six-class classification task using small and large datasets, respectively.

Parallel wideband digital up‐conversion architecture with efficiency

Owing to the limited processing speed of current digital signal processing devices, digital generated signal frequency and bandwidth based on digital up-conversion technique has long been a bottleneck. Interpolation on the baseband signal puts great pressure on the following filtering and mixing operation. In this study, an efficient parallel architecture is presented, which moves the interpolation behind the filtering and mixing, and adopts parallel numerically controlled oscillator (NCO) arrays and poly-phase low-pass filter arrays to achieve the anticipated orthogonal mixing signal and prototype filter. Parallel NCO decomposition principle and mathematical derivation are elaborated, and realisation of the poly-phase filter arrays is also discussed. The proposed post-interpolation architecture can effectively relieve the filtering and mixing pressure including operation rate and computational complexity, which will benefit the hardware implementation. In the end, verification test of signal up-conversion with 400 MHz bandwidth is launched to certify the architecture validity.

Hypertension Diagnosis Index for Discrimination of High-Risk Hypertension ECG Signals Using Optimal Orthogonal Wavelet Filter Bank.

Hypertension (HT) is an extreme increment in blood pressure that can prompt a stroke, kidney disease, and heart attack. HT does not show any symptoms at the early stage, but can lead to various cardiovascular diseases. Hence, it is essential to identify it at the beginning stages. It is tedious to analyze electrocardiogram (ECG) signals visually due to their low amplitude and small bandwidth. Hence, to avoid possible human errors in the diagnosis of HT patients, an automated ECG-based system is developed. This paper proposes the computerized segregation of low-risk hypertension (LRHT) and high-risk hypertension (HRHT) using ECG signals with an optimal orthogonal wavelet filter bank (OWFB) system. The HRHT class is comprised of patients with myocardial infarction, stroke, and syncope ECG signals. The ECG-data are acquired from physionet’s smart health for accessing risk via ECG event (SHAREE) database, which contains recordings of a total 139 subjects. First, ECG signals are segmented into epochs of 5 min. The segmented epochs are then decomposed into six wavelet sub-bands (WSBs) using OWFB. We extract the signal fractional dimension (SFD) and log-energy (LOGE) features from all six WSBs. Using Student’s t-test ranking, we choose the high ranked WSBs of LOGE and SFD features. We develop a novel hypertension diagnosis index (HDI) using two features (SFD and LOGE) to discriminate LRHT and HRHT classes using a single numeric value. The performance of our developed system is found to be encouraging, and we believe that it can be employed in intensive care units to monitor the abrupt rise in blood pressure while screening the ECG signals, provided this is tested with an extensive independent database.

Processing of the ECG orthogonal band-pass filter with the subsequent transfer in the phase plane

One of the methods of diagnosis and recognition of cardiovascular diseases is electrocardiography. The current state of diagnosis of cardiovascular diseases requires the development of new approaches to the analysis of electrocardiograms, there is a need to create new algorithms for processing information received from patients as a result of ECG removal. In this paper, it is proposed to use a band-pass orthogonal digital filter based on the Morlet wavelet function for processing electrocardiograms, which is not sensitive to the constant displacement of the input signal, does not have the Gibbs effect, which provides a better level of suppression in the barrier band obtained using the Fourier transform, followed by its transfer to the phase plane. The phase plane has found application in medicine for increase of reliability of the analysis and interpretation of an electrocardiogram for the purpose of increase of informativeness of cardiograms.

Automated detection of shockable and non-shockable arrhythmia using novel wavelet-based ECG features

Malignant arrhythmia can lead to sudden cardiac death (SCD). Shockable arrhythmia can be terminated with device electrical shock therapies. Ventricular-tachycardia (VT) and ventricular fibrillation (VF) are responsive to electrical anti-tachycardia pacing therapy and defibrillation which help to restore normal electrical and mechanical function of the heart. In contrast, non-shockable arrhythmia like asystole and bradycardia are not responsive to electric shock therapy. Distinguishing between shockable and non-shockable arrhythmia is an important diagnostic challenge that has practical clinical relevance. It is difficult to accurately differentiate between these two types of arrhythmia by manual inspection of electrocardiogram (ECG) segments within the short time duration before triggering the device for electrical therapy. Automated defibrillators are equipped with automatic shockable arrhythmia detection algorithms based on ECG morphological features, which may possess variable diagnostic performance depending on machine models. In our work, we have designed a robust system using wavelet decomposition filter banks for extraction of features from the ECG signal and then classifying the features. We believe this method will improve the accuracy of discriminating between shockable and non-shockable arrhythmia compared with existing conventional algorithms. We used a novel three channel orthogonal wavelet filter bank, which extracted features from ECG epochs of duration 2 s to distinguish between shockable and non-shockable arrhythmia. The fuzzy, Renyi and sample entropies are extracted from the various wavelet coefficients and fed to support vector machine (SVM) classifier for automated classification. We have obtained an accuracy of 98.9%, sensitivity and specificity of 99.08% and 97.11.9%, respectively, using 10-fold cross validation. The area under the receiver operating characteristic has been found to be 0.99 with F1-score of 0.994. The system developed is more accurate than the existing algorithms. Hence, the proposed system can be employed in automated defibrillators inside and outside hospitals for emergency revival of patients suffering from SCD. These automated defibrillators can also be implanted inside the human body for automatic detection of potentially fatal shockable arrhythmia and to deliver an appropriate electric shock to the heart.

Design of a Simple Orthogonal Multiwavelet Filter by Matrix Spectral Factorization

We consider the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization (MSF). As a test problem, we construct a simple matrix product filter with desirable properties, and factor it using Bauer's method, which in this case can be done in closed form. The corresponding orthogonal multiwavelet function is derived using algebraic techniques which allow symmetry to be considered. This leads to the known orthogonal multiwavelet SA1, which can also be derived directly. We also give a lifting scheme for SA1, investigate the influence of the number of significant digits in the calculations, and show some numerical experiments.

Novel Method for Prostate Cancer Detection Using Super Pixel and ANN Algorithm

Angiogenesis assumes a key job in prostate malignancy development. PCA stills lacks in tool for detection for prostate cancer. Cancer angiogenesis can be imaged by using super pixel segmentation and ANN algorithm. The prostate system is relies on the automatic 3D segmentation used for transrectal ultrasound images. The statistical texture and multi-atlas registration used for TRUS images. The transrectal ultrasound takes 15-30 minutes to complete the procedure. TRUS images is used to extract the size and shape of the prostate. The multi-atlas registration include TRUS images from previous images. The orthogonal gabor filter is utilized to separate the highlighted portion of the image in the database. The extracted feature is used to train Artificial Neural Network and segmented using super pixel segmentation. 3D segmentation is used to detect the tumor cells in invasive manner. The proposed work used to distinguish between the benign and malignant tumor The proposed work combination of targeted biopsy and systematic biopsy provides a higher detection rate.

Design of orthogonal graph filter bank with known eigenvalues of Laplacian matrix

In the conventional designs of orthogonal graph filter bank, both eigenvalues and eigenvectors of Laplacian matrix are assumed to be unknown such that graph filter bank can be efficiently implemented by using polynomial graph filters; that is, the output signal at each vertex is computed only from the signal at that vertex and its K -hop neighbourhoods. However, the disadvantage of these methods is that the designed orthogonal filter bank does not have the exact perfect reconstruction (PR). In this study, the authors first assume that the eigenvalues of Laplacian matrix are known but eigenvectors are still unknown. Then, the orthogonal graph filter bank is designed by solving the simultaneous equation or Lagrange multiplier method such that the PR condition at all eigenvalues can be achieved for a given graph structure. Although the proposed filter bank is a graph-structure-dependent design, it can be efficiently implemented by using polynomial graph filters. Finally, experimental results are shown to demonstrate the effectiveness of the proposed design method.

Development of an adaptive and explicit dual model predictive controller based on generalized orthogonal basis filters

A significant fraction of industrial MPC schemes employs linear prediction models. Closed loop performance of a linear model based MPC scheme can deteriorate over a period of time if the prediction model is not updated to account for the changing operating conditions. An effective way of handling this problem is to employ dual control, which directs the plant output towards a reference setpoint and simultaneously injects probing signals into the plant to get information-rich data which can be used for model identification under closed loop conditions. In this work, two multivariable adaptive dual MPC (ADMPC) schemes are developed based on MISO output error models that are parameterized using generalized orthonormal basis filters (GOBF). A nominal model is initially developed using offline identification exercise. The Fourier coefficients of the GOBF models are subsequently updated online using recursive parameter estimators. Also, to deal with large magnitude changes in the operating conditions, a shifting time window based approach is developed that can track variations of the GOBF poles online. To begin with, starting from a stochastic infinite horizon constrained optimal control problem, a computationally tractable finite horizon surrogate of the optimal control problem is derived. The surrogate problem includes terms that are sensitive to the parameter covariance. Based on the surrogate optimal control problem, two variants of ADMPC are proposed, viz. one that uses a fixed Fourier basis and another that uses a time varying Fourier basis. The effectiveness of the ADMPC schemes is evaluated by conducting stochastic simulations and experimental studies on the benchmark quadruple tank process. Analysis of the simulation results reveals that the proposed ADMPC schemes are able to achieve better tracking and regulatory performances when compared to the conventional adaptive MPC (AMPC). The simulation exercise also reveals that the proposed approach provides sufficient degrees of freedom to excite the plant in the closed loop for generating information-rich data for online model update. Experimental validation demonstrates that the proposed ADMPC is able to inject higher levels of input excitation throughout servo and regulatory responses with excitation levels similar to excitation levels used in the open loop identification experiments.

Research on Multi-stage Noise Reduction Method of NMR Logging Signal

By inversion calculation of T2 spectrum of echo string, the permeability, saturation, fluid type and other important parameters of porous media can be obtained. However, since the inversion algorithm itself is susceptible to noise signal [1], improving the SNR level of echo signal has been one of the key problems in the application of low-field NMR technology. In order to obtain more accurate analysis results, the corresponding noise reduction method needs to be developed. In the past, the research on noise reduction of NMR signal mainly focused on echo string. This paper constructs a complete NMR signal model and discusses the de-noising of echo and echo string. Aiming at noise reduction of echo, FIR filter and Orthogonal Modulation Filter(OMF) are discussed. Aiming at the de-noising of echo string, this paper proposes an improved CEEMD threshold de-noising, and makes a comparative analysis with the heuristic threshold de-noising based on sym4 wavelet and EMD threshold de-noising proposed by predecessors. It is found that the method proposed in this paper can invert the more accurate T2 spectrum while improving the SNR.

Fault feature extraction method based on EWT-SMF and MF-DFA for valve fault of reciprocating compressor

According to the nonlinearity and nonstationarity characteristics of reciprocating compressor vibration signal, a fault feature extraction method of reciprocating compressor based on the empirical wavelet transform (EWT) and state-adaptive morphological filtering (SMF) is proposed. Firstly, an adaptive empirical wavelet transform was used to divide the Fourier spectrum by constructing a scale-space curve, and an appropriate orthogonal wavelet filter bank was constructed to extract the AM-FM component with a tightly-supported Fourier spectrum. Then according to the impact characteristic of the reciprocating compressor vibration signal, the morphological structural elements were constructed with the characteristics of the signal to perform state-adaptive morphological filtering on the partitioned modal functions. Finally, the MF-DFA method of the modal function was quantitatively analyzed and the fault identification was performed. By analyzing the experimental data, it can be shown that the method can effectively identify the fault type of reciprocating compressor valve.

Design and implementation of a novel low complexity symmetric orthogonal wavelet filter‐bank

The design of wavelet filter-bank in real continuum domain demands infinite precision to achieve perfect reconstruction (PR). The computations with irrational coefficients in orthogonal filters require a large amount of hardware that result in increased power dissipation, huge memory requirements and reduction in speed of operation. This paper presents a new approach to obtain a complete dyadic (low complexity) 6-tap orthogonal symmetric wavelet filter-bank (FB) with near perfect reconstruction. This is achieved by slightly altering the PR conditions to make orthogonal filters symmetric and to obtain complete dyadic filter coefficients. The proposed wavelet FB has reduced dynamic power dissipation and significantly reduced adder and shifter count. The VLSI architecture of the proposed FB is designed and implemented on Kintex-7 FPGA. The architectural design is carried out using Verilog and functional simulation and synthesis are executed using Vivado 2016.4 software. The proposed FB dissipates 114mW dynamic power and requires only 5 adders and 3 shifters. The effectiveness of the proposed wavelet is verified in three different applications namely image compression, iris recognition system and orthogonal frequency division multiplexing (OFDM). The proposed wavelet FB gives comparable performance in image compression and attains superior performance in iris recognition system (feature extraction) and OFDM.