scholarly journals Pemrosessan Sinyal Waktu Diskrit Menggunakan Compressive Sensing Berdasarkan Algoritma Pemulihan L1

Electrician ◽  
2019 ◽  
Vol 13 (3) ◽  
Author(s):  
Umi Murdika ◽  
Lukmanul Hakim
Keyword(s):  
Signal Processing ◽  
Compressive Sensing ◽  
Discrete Time ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Signal Recovery ◽  
Original Signal ◽  
L1 Norm ◽  
Linear Measurements ◽  
Time Signals

Abstrak, — Metode Compressive Sensing merupakan metode yang banyak diaplikasikan pada pemrosesan sinyal. Kemampuan dan keunggulan metode ini mampu merekonstruksi sinyal dengan masukan yang terbatas. Makalah ini bertujuan menggunakan metode Compressive Sensing dalam mengolah sinyal digital waktu diskrit. Keutaman dari metode CS ini adalah memberikan perkiraan sinyal asli dari sejumlah kecil pengukuran linier inkoheren dengan memanfaatkan sifat kejarangannya Penyelesaian dengan metode Compressive Sensing menggunakan pendekatan sinyal sebagai kombinasi linier dari fungsi dasar yang merupakan matriks koefisien jarang (sparse matrix). Pemulihan sinyal dilakukan dengan meminimalkan ℓ1-norm dari persamaan sistem tersebut. Makalah ini menunjukkan bahwa dengan metode yang diterapkan pada pemrosessan sinyal, hanya dengan jumlah sinyal yang terbatas dapat dikembalikan lagi mendekati  dengan sinyal aslinya. Dengan perbedaan antara sinyal hasil pemulihan dengan sinyal asli yang cukup kecil. Kata kunci — Compressive Sensing, L1-norm, sinyal  waktu diskrit  pemulihan sinyal,  sinyal jarang.   Abstract — Compressive Sensing is a method that is widely applied to signal processing. The ability and superiority of this method is able to reconstruct signals with limited input. This paper aims to use the Compressive Sensing method in processing discrete time signals. The advantage of this CS method is to provide an original signal estimate from a small number of incoherent linear measurements by utilizing the sparsity properties. Solution using the Compressive Sensing method uses the signal approach as a linear combination of the basic functions which are sparse matrices. Signal recovery is done by minimizing L1-norm of the system equation. This paper shows that with the method applied to signal processing, a limited number of measurement signals can be returned close to the original signal. With the difference between the recovery signal and the original signal which is quite small. Keyword — Compressive Sensing, L1-norm, discrete time signals, recovery signal, sparse signal.

scholarly journals Hybrid Optical Cryptography and Compressive Sensing Based on Orthogonal Matching Pursuit

2018 ◽  
Author(s):  
Ertan Atar ◽  
Okan Ersoy
Keyword(s):  
Signal Processing ◽  
Compressive Sensing ◽  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Alternative Solution ◽  
Linear Measurements ◽  
Encrypt Data ◽  
Signal Vector

Compressive sensing (CS) is a technique that allows a signal vector to be reconstructed with a number of linear measurements far fewer than its size. In this study, optical hybrid cryptography with simultaneous compressive sensing based on orthogonal matching pursuit (OMP) is proposed as an alternative solution to the two important problems in communications, namely, effective / efficient / signal processing and secure encryption/decrypton. The whole system is able to both compress and encrypt data with attack immunity.

Digital Filters

2009 ◽  
pp. 364-372
Author(s):  
Gordana Jovanovic Dolecek
Keyword(s):  
Signal Processing ◽  
Discrete Time ◽  
Mathematical Representation ◽  
Time Signal ◽  
Digital Signals ◽  
Video Signals ◽  
Time Signals ◽  
Time Distance ◽  
Independent Variable ◽  
Distance Position

A signal is defined as any physical quantity that varies with changes of one or more independent variables, and each can be any physical value, such as time, distance, position, temperature, or pressure (Elali, 2003; Smith, 2002). The independent variable is usually referred to as “time”. Examples of signals that we frequently encounter are speech, music, picture, and video signals. If the independent variable is continuous, the signal is called continuous-time signal or analog signal, and is mathematically denoted as x(t). For discrete-time signals, the independent variable is a discrete variable; therefore, a discrete-time signal is defined as a function of an independent variable n, where n is an integer. Consequently, x(n) represents a sequence of values, some of which can be zeros, for each value of integer n. The discrete–time signal is not defined at instants between integers, and it is incorrect to say that x(n) is zero at times between integers. The amplitude of both the continuous and discrete-time signals may be continuous or discrete. Digital signals are discrete-time signals for which the amplitude is discrete. Figure 1 illustrates the analog and the discrete-time signals. Most signals that we encounter are generated by natural means. However, a signal can also be generated synthetically or by computer simulation (Mitra, 2006). Signal carries information, and the objective of signal processing is to extract useful information carried by the signal. The method of information extraction depends on the type of signal and the nature of the information being carried by the signal. “Thus, roughly speaking, signal processing is concerned with the mathematical representation of the signal and algorithmic operation carried out on it to extract the information present,’’ (Mitra, 2006, pp. 1).

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Irena Orović ◽  
Vladan Papić ◽  
Cornel Ioana ◽  
Xiumei Li ◽  
Srdjan Stanković
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Signal Acquisition ◽  
Transform Domain ◽  
Hermite Transform ◽  
Time Frequency ◽  
Reconstruction Methods ◽  
Fourier Transform Domain

Compressive sensing has emerged as an area that opens new perspectives in signal acquisition and processing. It appears as an alternative to the traditional sampling theory, endeavoring to reduce the required number of samples for successful signal reconstruction. In practice, compressive sensing aims to provide saving in sensing resources, transmission, and storage capacities and to facilitate signal processing in the circumstances when certain data are unavailable. To that end, compressive sensing relies on the mathematical algorithms solving the problem of data reconstruction from a greatly reduced number of measurements by exploring the properties of sparsity and incoherence. Therefore, this concept includes the optimization procedures aiming to provide the sparsest solution in a suitable representation domain. This work, therefore, offers a survey of the compressive sensing idea and prerequisites, together with the commonly used reconstruction methods. Moreover, the compressive sensing problem formulation is considered in signal processing applications assuming some of the commonly used transformation domains, namely, the Fourier transform domain, the polynomial Fourier transform domain, Hermite transform domain, and combined time-frequency domain.

scholarly journals Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

2012 ◽  
Vol 20 (3) ◽  
pp. 241-255 ◽  
Author(s):  
Eric Bavier ◽  
Mark Hoemmen ◽  
Sivasankaran Rajamanickam ◽  
Heidi Thornquist
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Direct Methods ◽  
Iterative Solvers ◽  
Software Project ◽  
Sparse Linear Systems ◽  
Scalar Type ◽  
Mixed Precision

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

scholarly journals Application-based fault tolerance techniques for sparse matrix solvers

2017 ◽  
Vol 32 (5) ◽  
pp. 627-640
Author(s):  
Simon McIntosh–Smith ◽  
Rob Hunt ◽  
James Price ◽  
Alex Warwick Vesztrocy
Keyword(s):  
Fault Tolerance ◽  
High Performance Computing ◽  
High Performance ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Error Correcting Codes ◽  
Computing Systems ◽  
Hardware Costs ◽  
Extreme Scale ◽  
Performance Computing

High-performance computing systems continue to increase in size in the quest for ever higher performance. The resulting increased electronic component count, coupled with the decrease in feature sizes of the silicon manufacturing processes used to build these components, may result in future exascale systems being more susceptible to soft errors caused by cosmic radiation than in current high-performance computing systems. Through the use of techniques such as hardware-based error-correcting codes and checkpoint-restart, many of these faults can be mitigated at the cost of increased hardware overhead, run-time, and energy consumption that can be as much as 10–20%. Some predictions expect these overheads to continue to grow over time. For extreme scale systems, these overheads will represent megawatts of power consumption and millions of dollars of additional hardware costs, which could potentially be avoided with more sophisticated fault-tolerance techniques. In this paper we present new software-based fault tolerance techniques that can be applied to one of the most important classes of software in high-performance computing: iterative sparse matrix solvers. Our new techniques enables us to exploit knowledge of the structure of sparse matrices in such a way as to improve the performance, energy efficiency, and fault tolerance of the overall solution.

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