scholarly journals Discrete sampling theorem to Shannon’s sampling theorem using the hyperreal numbers R

2021 ◽  
Vol 28 (2) ◽  
pp. 163-182
Author(s):  
José L. Simancas-García ◽  
Kemel George-González
Keyword(s):  
Computational Cost ◽  
Number System ◽  
Sampling Theorem ◽  
Discrete Sampling ◽  
Sampled Signal ◽  
Speed Up ◽  
Shannon’S Sampling Theorem ◽  
The Difference ◽  
Band Limited ◽  
Hyperreal Numbers

Shannon’s sampling theorem is one of the most important results of modern signal theory. It describes the reconstruction of any band-limited signal from a finite number of its samples. On the other hand, although less well known, there is the discrete sampling theorem, proved by Cooley while he was working on the development of an algorithm to speed up the calculations of the discrete Fourier transform. Cooley showed that a sampled signal can be resampled by selecting a smaller number of samples, which reduces computational cost. Then it is possible to reconstruct the original sampled signal using a reverse process. In principle, the two theorems are not related. However, in this paper we will show that in the context of Non Standard Mathematical Analysis (NSA) and Hyperreal Numerical System R, the two theorems are equivalent. The difference between them becomes a matter of scale. With the scale changes that the hyperreal number system allows, the discrete variables and functions become continuous, and Shannon’s sampling theorem emerges from the discrete sampling theorem.

A regularized two-dimensional sampling algorithm

2018 ◽  
Vol 26 (1) ◽  
pp. 67-84
Author(s):  
Weidong Chen
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Sampling Theorem ◽  
Dimensional Case ◽  
Tikhonov Regularization Method ◽  
Two Dimensional ◽  
Sampling Algorithm ◽  
Shannon’S Sampling Theorem ◽  
Band Limited

AbstractIn this paper, a regularized sampling algorithm for band-limited signals is presented in the two-dimensional case. The convergence of the regularized sampling algorithm is studied and compared with Shannon’s sampling theorem and the Tikhonov regularization method by some examples.

scholarly journals A Stochastic Model for Block Segmentation of Images Based on the Quadtree and the Bayes Code for It

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 991
Author(s):  
Yuta Nakahara ◽  
Toshiyasu Matsushima
Keyword(s):  
Computational Cost ◽  
Block Size ◽  
Input Image ◽  
Generative Model ◽  
Image Size ◽  
Variable Block ◽  
General Data ◽  
The Difference ◽  
Segmentation Of Images ◽  
Target Data

In information theory, lossless compression of general data is based on an explicit assumption of a stochastic generative model on target data. However, in lossless image compression, researchers have mainly focused on the coding procedure that outputs the coded sequence from the input image, and the assumption of the stochastic generative model is implicit. In these studies, there is a difficulty in discussing the difference between the expected code length and the entropy of the stochastic generative model. We solve this difficulty for a class of images, in which they have non-stationarity among segments. In this paper, we propose a novel stochastic generative model of images by redefining the implicit stochastic generative model in a previous coding procedure. Our model is based on the quadtree so that it effectively represents the variable block size segmentation of images. Then, we construct the Bayes code optimal for the proposed stochastic generative model. It requires the summation of all possible quadtrees weighted by their posterior. In general, its computational cost increases exponentially for the image size. However, we introduce an efficient algorithm to calculate it in the polynomial order of the image size without loss of optimality. As a result, the derived algorithm has a better average coding rate than that of JBIG.

scholarly journals Low-Frequency Signal Sampling Method Implemented in a PLC Controller Dedicated to Applications in the Monitoring of Selected Electrical Devices

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 442
Author(s):  
Marcin Jaraczewski ◽  
Ryszard Mielnik ◽  
Tomasz Gębarowski ◽  
Maciej Sułowicz
Keyword(s):  
Power System ◽  
Reactive Power ◽  
Low Frequency ◽  
Sampling Frequency ◽  
Electrical Signal ◽  
Distortion Factor ◽  
Electrical Devices ◽  
Frequency Sampling ◽  
Sampled Signal ◽  
Band Limited

High requirements for power systems, and hence for electrical devices used in industrial processes, make it necessary to ensure adequate power quality. The main parameters of the power system include the rms-values of the current, voltage, and active and reactive power consumed by the loads. In previous articles, the authors investigated the use of low-frequency sampling to measure these parameters of the power system, showing that the method can be easily implemented in simple microcontrollers and PLCs. This article discusses the methods of measuring electrical quantities by devices with low computational efficiency and low sampling frequency up to 1 kHz. It is not obvious that the signal of 50–500 Hz can be processed using the sampling frequency of fs = 47.619 Hz because it defies the Nyquist–Shannon sampling theorem. This theorem states that a reconstruction of a sampled signal is only guaranteed possible for a bandlimit fmax < fs, where fmax is the maximum frequency of a sampled signal. Therefore, theoretically, neither 50 nor 500 Hz can be identified by such a low-frequency sampling. Although, it turns out that if we have a longer period of a stable multi-harmonic signal, which is band-limited (from the bottom and top), it allows us to map this band to the lower frequencies, thus it is possible to use the lower sampling ratio and still get enough precise information of its harmonics and rms value. The use of aliasing for measurement purposes is not often used because it is considered a harmful phenomenon. In our work, it has been used for measurement purposes with good results. The main advantage of this new method is that it achieves a balance between PLC processing power (which is moderate or low) and accuracy in calculating the most important electrical signal indicators such as power, RMS value and sinusoidal-signal distortion factor (e.g., THD). It can be achieved despite an aliasing effect that causes different frequencies to become indistinguishable. The result of the research is a proposal of error reduction in the low-frequency measurement method implemented on compact PLCs. Laboratory tests carried out on a Mitsubishi FX5 compact PLC controller confirmed the correctness of the proposed method of reducing the measurement error.

scholarly journals Dynamic maintenance model for high average-utility pattern mining with deletion operation

2021 ◽  
Author(s):  
Jimmy Ming-Tai Wu ◽  
Qian Teng ◽  
Shahab Tayeb ◽  
Jerry Chun-Wei Lin
Keyword(s):  
Pattern Mining ◽  
Computational Cost ◽  
Practical Applications ◽  
Itemset Mining ◽  
Dynamic Databases ◽  
Speed Up ◽  
Dynamic Maintenance ◽  
Average Utility ◽  
High Utility ◽  
Maintenance Model

AbstractThe high average-utility itemset mining (HAUIM) was established to provide a fair measure instead of genetic high-utility itemset mining (HUIM) for revealing the satisfied and interesting patterns. In practical applications, the database is dynamically changed when insertion/deletion operations are performed on databases. Several works were designed to handle the insertion process but fewer studies focused on processing the deletion process for knowledge maintenance. In this paper, we then develop a PRE-HAUI-DEL algorithm that utilizes the pre-large concept on HAUIM for handling transaction deletion in the dynamic databases. The pre-large concept is served as the buffer on HAUIM that reduces the number of database scans while the database is updated particularly in transaction deletion. Two upper-bound values are also established here to reduce the unpromising candidates early which can speed up the computational cost. From the experimental results, the designed PRE-HAUI-DEL algorithm is well performed compared to the Apriori-like model in terms of runtime, memory, and scalability in dynamic databases.

scholarly journals Combining Acceleration Techniques for Low-Dose X-Ray Cone Beam Computed Tomography Image Reconstruction

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Hsuan-Ming Huang ◽  
Ing-Tsung Hsiao
Keyword(s):  
Computed Tomography ◽  
Image Reconstruction ◽  
Low Dose ◽  
Computational Cost ◽  
Reconstruction Algorithm ◽  
Reconstruction Algorithms ◽  
Acceleration Techniques ◽  
Reconstruction Methods ◽  
Speed Up ◽  
Phantom Studies

Background and Objective. Over the past decade, image quality in low-dose computed tomography has been greatly improved by various compressive sensing- (CS-) based reconstruction methods. However, these methods have some disadvantages including high computational cost and slow convergence rate. Many different speed-up techniques for CS-based reconstruction algorithms have been developed. The purpose of this paper is to propose a fast reconstruction framework that combines a CS-based reconstruction algorithm with several speed-up techniques.Methods. First, total difference minimization (TDM) was implemented using the soft-threshold filtering (STF). Second, we combined TDM-STF with the ordered subsets transmission (OSTR) algorithm for accelerating the convergence. To further speed up the convergence of the proposed method, we applied the power factor and the fast iterative shrinkage thresholding algorithm to OSTR and TDM-STF, respectively.Results. Results obtained from simulation and phantom studies showed that many speed-up techniques could be combined to greatly improve the convergence speed of a CS-based reconstruction algorithm. More importantly, the increased computation time (≤10%) was minor as compared to the acceleration provided by the proposed method.Conclusions. In this paper, we have presented a CS-based reconstruction framework that combines several acceleration techniques. Both simulation and phantom studies provide evidence that the proposed method has the potential to satisfy the requirement of fast image reconstruction in practical CT.

scholarly journals Fast Image Registration for Spacecraft Autonomous Navigation Using Natural Landmarks

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Yun-Hua Wu ◽  
Lin-Lin Ge ◽  
Feng Wang ◽  
Bing Hua ◽  
Zhi-Ming Chen ◽  
...  
Keyword(s):  
Image Registration ◽  
Autonomous Navigation ◽  
Computational Cost ◽  
Segmentation Algorithm ◽  
Speeded Up Robust Features ◽  
Speed Up ◽  
Random Sample Consensus ◽  
Invariant Properties ◽  
Low Computational Cost ◽  
Ransac Algorithm

In order to satisfy the real-time requirement of spacecraft autonomous navigation using natural landmarks, a novel algorithm called CSA-SURF (chessboard segmentation algorithm and speeded up robust features) is proposed to improve the speed without loss of repeatability performance of image registration progress. It is a combination of chessboard segmentation algorithm and SURF. Here, SURF is used to extract the features from satellite images because of its scale- and rotation-invariant properties and low computational cost. CSA is based on image segmentation technology, aiming to find representative blocks, which will be allocated to different tasks to speed up the image registration progress. To illustrate the advantages of the proposed algorithm, PCA-SURF, which is the combination of principle component analysis and SURF, is also analyzed in this paper for comparison. Furthermore, random sample consensus (RANSAC) algorithm is applied to eliminate the false matches for further accuracy improvement. The simulation results show that the proposed strategy obtains good results, especially in scaling and rotation variation. Besides, CSA-SURF decreased 50% of the time in extraction and 90% of the time in matching without losing the repeatability performance by comparing with SURF algorithm. The proposed method has been demonstrated as an alternative way for image registration of spacecraft autonomous navigation using natural landmarks.

scholarly journals Finite element method completely implemented for graphic processor units using parallel algorithm libraries

2017 ◽  
Vol 33 (1) ◽  
pp. 53-66 ◽  
Author(s):  
Franz Pichler ◽  
Gundolf Haase
Keyword(s):  
Finite Element ◽  
Graphics Processing Unit ◽  
Computational Cost ◽  
Processing Unit ◽  
Time Step ◽  
Device Architecture ◽  
Transient Problems ◽  
Speed Up ◽  
Automotive Batteries ◽  
Graphics Processing

A finite element code is developed in which all of the computationally expensive steps are performed on a graphics processing unit via the THRUST and the PARALUTION libraries. The code focuses on the simulation of transient problems where the repeated computations per time-step create the computational cost. It is used to solve partial and ordinary differential equations as they arise in thermal-runaway simulations of automotive batteries. The speed-up obtained by utilizing the graphics processing unit for every critical step is compared against the single core and the multi-threading solutions which are also supported by the chosen libraries. This way a high total speed-up on the graphics processing unit is achieved without the need for programming a single classical Compute Unified Device Architecture kernel.

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