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Analog Signal Conditioning in Instrumentation
Published in Robert B. Northrop, Introduction to Instrumentation and Measurements, 2018
The same biquad filter can be used as a tuned BPF. In this case, the output is taken from the V4 node. The transfer function again can be found by the application of Mason’s rule: () V4Vs=−sR3CR2/(R1R2)s2R32C2+(sR3CR/R2)+1
Dynamic System Response
Published in Arthur G.O. Mutambara, Design and Analysis of Control Systems, 2017
Three main mathematical approaches are used to obtain the system response: direct solution of differential equations in the time domain, the use of the Laplace transform to solve differential equations in the frequency domain, and the deduction of system behavior from the system transfer function. The Laplace transform is a mathematical tool for transforming linear differential equations into an easier-to-manipulate algebraic form. In this domain, the differential equations are easily solved and the solutions are converted back into the time domain to give the system response. The transfer function was introduced in Chapter 2 as a modeling tool. The major advantage of this form of the dynamic system model is that the system response can be easily obtained from it. From the transfer function the system poles and zeros can be identified and these provide information about the characteristics of the system response. The location of the poles and zeros can then be manipulated to achieve certain desired characteristics or eliminate undesirable ones. In addition to the direct mathematical derivation of the transfer function, there are two visual tools that can be employed to derive it. The first is the block diagram, which was introduced in Chapter 2 and the other is the signal flow graph. The latter method consists of characterizing the system by a network of directed branches and associated gains (transfer functions) connected to nodes. Mason’s rule is used to relate the graph to the algebra of the system simultaneous equations, thus determining the system transfer function.
Structures for the Realization of Discrete-Time Systems
Published in Anastasia Veloni, Nikolaos I. Miridakis, Erysso Boukouvala, Digital and Statistical Signal Processing, 2018
Anastasia Veloni, Nikolaos I. Miridakis, Erysso Boukouvala
Mason’s gain formula (1953), or Mason’s rule, is a method for deriving the transfer function of a system through its SFG. By applying Mason’s rule there is no need to use block diagram reduction. The mathematical formulation is given in Equation 4.19: H(z)=∑n=1kTnDnD
Supply chain delivery performance improvement: a white-box perspective
Published in International Journal of Production Research, 2023
Liangyan Tao, Ailin Liang, Maxim A. Bushuev
From the CF-GERT analytical algorithm, Mason’s rule is employed to obtain the equivalent transfer function of the network. After Mason’s rule is used, each transfer function (W) is substituted by its expression from Table 4. Then Theorem 1 indicates that the success probability is , and the equivalent characteristic function of the CF-GERT network is .