Recursive Pyramid Algorithm-Based Discrete Wavelet Transform for Reactive Power Measurement in Smart Meters

A class of VLSI architectures based on linear systolic arrays, for computing the 1-D Discrete Wavelet Transform (DWT), is presented. The various architectures of this class differ only in the design of their routing networks, which could be systolic, semisystolic, or RAM-based. These architectures compute the Recursive Pyramid Algorithm, which is a reformulation of Mallat's pyramid algorithm for the DWT. The DWT is computed in real time (running DWT), using just N/sub w/(J-1) cells of storage, where N/sub w/ is the length of the filter and J is the number of octaves. They are ideally suited for single-chip implementation due to their practical I/O rate, small storage, and regularity. The N-point 1-D DWT is computed in 2N cycles. The period can be reduced to N cycles by using N/sub w/ extra MAC's. Our architectures are shown to be optimal in both computation time and in area. A utilization of 100% is achieved for the linear array. Extensions of our architecture for computing the M-band DWT are discussed. Also, two architectures for computing the 2-D DWT (separable case) are discussed. One of these architectures, based on a combination of systolic and parallel filters, computes the N/sup 2/-point 2-D DWT, in real time, in N/sup 2/+N cycles, using 2NN/sub w/ cells of storage. >

This paper presents efficient VLSI architectures for real time processing of separable convolution and lifting based 2-D discrete wavelet transform (DWT). Convolution based architecture uses partitioning algorithm based on the state space representation method and lifting based architecture applies pipelining to each lifting step. Both architectures use recursive pyramid algorithm(RPA) scheduling that intersperses both the row and column operations of the second and following levels among column operations of the first level without using additional filter for row operations of the second and following levels. As a result, proposed architectures have smaller hardware complexity compared to that of other conventional separable architectures with comparable throughput.

Based on the discrete wavelet transformation (DWT), we present a pixelized method of estimating the power spectra of galaxy samples. With local properties of wavelet both in physical and wavenumber spaces, DWT power spectrum is equal to the corresponding band average of Fourier power spectrum. The DWT estimator is optimized in the sense that the spatial resolution is adaptive automatically to the perturbation wavelength to be studied. Under the assumption of ergodicity, the spatial average of local DWT fluctuation modes provides a fair estimation of the ensemble average. We test DWT spectra of four typical cold dark matter (CDM) structure formation models with numerical simulations. To consider the infections of various observation effects to the DWT spectra, we introduce irregular survey geometries, a given sampling rate, radial selection effects and redshift distortion effects into our mock samples. The numerical results show that, owing to its local properties, DWT spectrum is less affected by the sampling rate, survey geometry, and statistical ensemble fluctuations. With fast wavelet decomposition algorithm, DWT can be used to analyze large survey samples, which is of direct significance in precise measurement of the cosmological parameters from the galaxy redshift surveys of next generation.

To derive adequate octave band components for perfect reconstruction in the inverse 2-D discrete wavelet transform (DWT) process, this paper presents a new VLSI architecture for 2-D DWT implementation by using the periodized wavelets and considering the separable case. The principal idea of the architecture design is based on the concept of batch processing. The batch processing design method can make handling the boundary data easier and provide easier controller design than the interleaving techniques. The latency of the architecture is 1. An example of using the l=4, l denotes filter length, is illustrated. The architecture can be easily expanded to a general case of the 2-D DWT including different filter length and arbitrary terminate decomposition level. The overall architecture has been successfully simulated with 14 data bits of Verilog behavioral model simulation to confirm the feasibility.

Recently the saving of energy has become an important consideration in electric power line systems. One method for saving energy is the reduction of reactive energy loss in electric equipment. Therefore, the measurement of reactive energy is becoming increasingly important. The developed reactive energy transducer is composed of a typical 90° RC phase shifter using an operational amplifier, a multiplier and a DC current to pulse frequency converter of which the output pulses are counted for measurement of the reactive energy. Generally, as the output amplitude of the 90° phase shifter varies with the line frequency, this variation must be compensated for in precise measurement. In the developed reactive energy transducer, the variation of the amplitude of the shifter is compensated for by changing the conversion coefficient of the DC current to pulse frequency converter.

This paper demonstrates the merits of nested Compressive Sensing (CS) approach for Electrocardiogram (ECG) signals using discrete wavelet transform (DWT) and discrete cosine transform (DCT) as sensing matrix and sparsifying matrix. The implementation of CS framework is done using Gradient Projection for Sparse Reconstruction (GPSR). It is tested on 9 ECG signals of different arrhythmia categories obtained from MITBIH and BIDMC dataset. It is analysed for 3 different combinations, case (1) DCT sensing and DWT sparsification, case (2) DWT sensing and DCT sparsification and case (3) DWT sensing and DWT sparsification. A novel hybrid nested CS approach is proposed as case (4) which is a combination of case (2) in higher level and case (1) in lower level. This nested method yields the best PRD of 1.39 for CR = 0.2 and performs better than all proposed cases. This proposed approach involves a fair method of discarding the measurements in all frequency band and performs better than the state of the art work when the sampling rate is reduced by 4 times for ECG signal 100.dat from MIT-BIH (Massachusetts Institute of Technology-Beth Israel Hospital) database for CR = 0.2. It is shown that the reconstruction time of the proposed nested CS approach is lesser than non-nested CS approach.

Technical losses of smart grids can be computed using the customer's smart meter measurements (active and reactive energy) and the energy measurement registered by the Low Voltage (LV) supervisor deployed at secondary substations. However, in some LV networks, some customers do not provide information regarding the energy consumed and produced in real time. This fact complicates the calculation of technical losses because this information is necessary for estimating the load demand for this subset of customers. In this paper, a stochastic approach is proposed for the estimation of technical losses in smart grids under uncertain load demands (e.g., non-telemetered customers and uncertain smart meters readings). Load demand estimation of non-metered customers was performed by means of a top-down approach. Intra-hour load demand profiles of customers were synthetically generated by applying a Markov process. The data and network used in this process corresponded to the roll-out deployed by the Spanish Research and Development (R&D) demonstration project OSIRIS.

VLSI Implementation of Discrete Wavelet Transform for Lossless Compression of Medical Images

Simultaneous quantitative analysis of overlapping spectrophotometric signals using wavelet multiresolution analysis and partial least squares

Since the discrete wavelet transform (DWT) is a kind of multi-rate transform, it is difficult to design an optimal computation-time architecture for the DWT. In this paper, we propose a highly efficient VLSI architecture for the 1-D DWT decomposition. This architecture contains two stages of systolic decimation filter banks to guarantee a high throughput and an optimal computation time. Using this architecture, N-point samples with J resolution levels can be computed in N clock cycles spending only JL registers, where L denotes filter length. Due to its regular structure, this architecture can be easily scaled up with the tap size of the filters and the number of octaves. The performance of the proposed architecture will be verified by the successful implementation of a 4-tap 3-octave DWT VLSI chip.

In this research a special type of meter is developed which can measure various important parameters of electrical energy and as well as give users the access to cntrol the appliances which are connected to it through the designed android application. Initially measurement of the current is performed with the help of Hall Effect sensor, as this method is very accurate. In second part supply voltage is calculated with the help of transformer and DC biasing method. This method is also very accuratefor measurement of voltage. By multiplying the above measured current and voltage, apparent power is obtained. Finally, the energy parameter is obtained. In this research, a special type of meter is designed which can measure electrical current, voltage, power and energy with accuracy around 99%. These obtained parameter results will be directly uploaded to Google firebase which is connected to our android app. Any user having this application installed will take this reading live to their smart phones as well as their web browser

Ultrasonic metal welding (UMW) is widely used in industrial applications such as electric vehicle battery manufacturing and automotive body assembly. The joint quality of UMW is sensitive to a variety of undesired yet inevitable process disturbances such as tool condition and material surface condition. Online monitoring and control capabilities are critically needed to quickly detect process anomalies and adaptively adjust process parameters, thus ensuring satisfactory joint quality and reducing process variability. While existing research has developed online quality monitoring methods for UMW, the cost-effectiveness of hardware (sensors, data acquisition equipment, and edge-computing devices) and software (computational efficiency) in a monitoring system has not been investigated systematically. The cost-effectiveness of monitoring also decides the window during which control actions can be executed, thus ultimately influencing the joint quality. This paper presents a systematic study on three factors related to cost-effectiveness: (1) sensor selection, (2) sampling rate of data acquisition, and (3) signal fraction. A method based on discrete wavelet transformation (DWT) is used for automatic feature extraction due to its effectiveness in extracting both time-domain and frequency-domain information with varying signal lengths. We develop a multi-layer perceptron (MLP) classifier to process DWT-generated features and recognize two types of welding disturbances including tool condition and material surface condition. Case studies demonstrate that combining a suitable signal fraction with a subset of sensors leads to comparable performance to using all sensors at full length. Moreover, the interaction between the sampling rate and the signal fraction is investigated. Results confirm the feasibility of building an accurate monitoring system with limited sampling rate and signal fraction, which increases the window for real-time control.

In recent years the development and deployment of commercial Smart Meters in most households in developed countries have spread the appearance of certain applications and methods, mainly related to the fields of Smart Grids and Internet of Things, where Non-Intrusive Load Monitoring (NILM) is one of the most well-known. It takes advantage of the capability of Smart Meters to acquire the electrical signals of a household or building in real time, in order to implement a set of techniques oriented to disaggregate the power consumption, according to the different electrical loads plugged in the facility. Previous works are often based on a cloud-computing approach, where samples are transferred straightforwardly from the local meter to the cloud for further analysis. This implies that the sampling rates are low in order to keep the required bandwidth reduced, thus constraining the final performance achieved in the load identification. This work presents the design of a System-on-Chip (SoC) architecture based on a Field-Programmable Gate Array (FPGA) device that can be installed locally at the input of the electrical installation from a house or building. It is able to manage data rates at high sampling frequencies and to implement in real time those algorithms proposed for the electrical signal processing and load classification. Experimental results have preliminary validated the proposed architecture.

This paper proposes an efficient image reconstruction for compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) using Symlet 8 (sym8) wavelets with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT) which relies on computationally intensive convolution operations the LWT provides a faster sparse representation while preserving the sparsity crucial for CS. The proposed approach leverages a key insight: among the four subbands produced by the LWT namely the approximation (CA) and the detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Therefore, compressive sensing is applied exclusively to these detail subbands, while the CA subband is left uncompressed to retain essential low-frequency information. Experiments were conducted on both a natural test image (Lena) and a medical MRI scan, across image resolutions ranging from 200×200 to 512×512 pixels and sampling rates from 10% to 80%. Performance was assessed using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently demonstrate that ALISTA significantly outperforms SP and CoSaMP in both reconstruction fidelity and computational efficiency. At an 80% sampling rate, ALISTA achieves SSIM values of 0.99346 for Lena and 0.98 for the MRI image, compared to approximately 0.97 and 0.94, respectively, for the other two methods. Furthermore, ALISTA maintains remarkably low reconstruction times under 4 seconds even for 512×512-pixel images. These findings confirm that the ALISTA + LWT/sym8 combination offers the best trade-off between image quality and speed, exhibiting robustness across different image types and scales.

This paper proposes an efficient image reconstruction for compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) using Reverse Biorthogonal 6.8 (rbio6.8) wavelets with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT) which relies on computationally intensive convolution operations the LWT provides a faster sparse representation while preserving the sparsity crucial for CS. The proposed approach leverages a key insight: among the four subbands produced by the LWT namely the approximation (CA) and the detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Therefore, compressive sensing is applied exclusively to these detail subbands, while the CA subband is left uncompressed to retain essential low-frequency information. Experiments were conducted on both a natural test image (Lena) and a medical MRI scan, across image resolutions ranging from 200×200 to 512×512 pixels and sampling rates from 10% to 80%. Performance was assessed using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently demonstrate that ALISTA significantly outperforms SP and CoSaMP in both reconstruction fidelity and computational efficiency. At an 80% sampling rate, ALISTA achieves SSIM values of 0.99314 for Lena and 0.97688 for the MRI image, compared to approximately 0.97402 and 0.93577, respectively, for the other two methods. Furthermore, ALISTA maintains remarkably low reconstruction times under 4 seconds even for 512×512-pixel images. These findings confirm that the ALISTA + LWT/rbio6.8 combination offers the best trade-off between image quality and speed, exhibiting robustness across different image types and scales.