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Design of Actuator Servo Controller
Published in Abdullah Al Mamun, GuoXiao Guo, Chao Bi, Hard Disk Drive, 2017
Abdullah Al Mamun, GuoXiao Guo, Chao Bi
One advantage of numerical search method is that the cost function C can be of any type, such as ITAE, the Integral of the Time multiplied by the Absolute value of the Error, or a combination of probability of the stability, phase margin, time responses, etc, and is not limited to the quadratic cost functions or desired pole locations which yield closed-form solutions. When the field of search is sufficiently wide, non-gradient based method do not get stuck, but a gradient algorithm may, for complex cost functions with a multitude of local minima. For the case of RNS algorithm it also has the advantage of being very simple to implement. Its main steps are given below: The designer initiates the random search by defining the limits of the search space D.A random number generator selects points dk within D, where k = 1, 2, ..., Ns, is the number of search points.The value of J(dk) is tested for each k, and the point giving the lowest value is taken to be the estimate of the global minimizer, d*.
Perspectives on Digital Image Watermarking
Published in Roy Subhrajit Sinha, Basu Abhishek, Chattopadhya Avik, Intelligent Copyright Protection for Images, 2019
Roy Subhrajit Sinha, Basu Abhishek, Chattopadhya Avik
To improve the watermark payload, S. Banerjee proposed a new color image watermarking algorithm (Banerjee et al., 2015) based on the residue number system (RNS). RNS, developed from the Chinese remainder theorem of modular arithmetic, refers to a large integer dependent on a set of smaller numbers. In this watermarking procedure, the pixel values from three different watermark images are taken and inserted into the cover image. From the empirical results, the author concluded that the watermarks were imperceptibly embedded into the cover image and successfully extracted from it, offering both better payload values and robustness.
Digital Signal Processing with Field-Programmable Gate Array
Published in A. Arockia Bazil Raj, FPGA-Based Embedded System Developer's Guide, 2018
The residue numeral system (RNS) represents a large integer using a set of smaller integers to perform computations more efficiently [25,151,152]. The basic principle of the RNA is CRT and modular arithmetic, as discussed in the previous section. RNA-based computations and their operations are the mathematical ideas of Sun Tsu Suan-Ching, who lived in the fourth century. By applying this idea, a large integer can be decomposed into a set of smaller integers. The larger digit calculation can be performed as a series of smaller digit calculations that can be performed independently as well as in parallel. We discuss some examples to understand that how the RNS supports improving the speed of arithmetic operations. In most arithmetic systems, the speed is limited by the nature of arithmetic building blocks that make the logic decisions. For example, in the addition operation, a lower-order/intermediate carry can have a ripple effect on the subsequent/total sum. In the residue number system, the positional bases are relatively prime to each other; for example, the bases may be 2, 3 and 5, that is, prime numbers, a number that is divisible only by itself and 1, for example, 2, 3, 5, 7, 11, and so on. With these prime numbers, the maximum decimal number possible to perform RNS representation is computed by 2 × 3 × 5 = 30. This means that the decimal numbers 0 through 29 can be uniquely represented by the RNS with the bases of 2, 3 and 5. For example, in a (5,3,2) RNS, (3)10 is represented by (3 mod 5) = 3, (3 mod 3) = 0 and (3 mod 2) = 1; therefore, the RNS representation for (3)10 is (3,0,1). Suppose a decimal number is (28)10. Then, (28 mod 5) = 3, (28 mod 3) = 1 and (28 mod 2) = 0, and the RNS of (28)10 is (3,1,0).
Measuring 3- and 4-Moduli Sets Delay Per Bit in Residue Number System: A Survey
Published in IETE Journal of Research, 2023
Residue number system (RNS) is defined in terms of a set of integer moduli , … , , which are commonly pairwise prime to allow for maximal dynamic range (i.e. ). Carry propagation is limited to the width of parallel moduli; therefore, computations with high-speed and low-power dissipation are normally expected. As such, RNS is proper for digital signal and image processing [1, 2] and cryptography [1]. In addition, RNS is a practical implementing option for RSA and elliptic curve cryptography, which are the most popular public key systems [3, 4]. Indeed, complete computation of convolutional neural networks [5–7] in RNS would reduce cost and time, which are crucial factors.
Teaching redundant residue number system for electronics and computer students
Published in International Journal of Mathematical Education in Science and Technology, 2022
(residue number system): RNS is a numeral system to represent a binary number by smaller integers. The system is defined by a set of N positive and pairwise relatively prime moduli . A number X in the system is represented by , where and signifies the residue of X modulo mi. Any integer X in the range [0, M−1] has a unique representation, where is the dynamic range (DR) of the moduli set (Garner, 1959; Timarchi & Akbarzadeh, 2019).