China
Africa
Explore chapters and articles related to this topic
Analytical Modeling
Published in Clarence W. de Silva, Modeling of Dynamic Systems with Engineering Applications, 2023
A discrete-time signal is defined at a sequence of discrete time points of a continuous-time (analog) signal. Typically, it is obtained by discretizing (sampling) an analog signal, which is defined continuously in time (see Figure 3.2). Reading (or sampling) an analog signal at discrete time points is not the only way to generate a discrete-time signal. For example, a physical switching device may be activated in a discrete time sequence to generate discrete-time data. The time interval between two successive data points is the sampling periodΔT. In typical practical situations such as digital hardware (or digital computer), the sampling period is a constant. The sampling ratefs is the inverse of the sampling period: fs=1ΔT
Storage and transmission of spatial sound signals
Published in Bosun Xie, Spatial Sound, 2023
Sampling is performed to represent a continuous time signal by its values at discrete times, resulting in discrete time samples or signals (sequence). According to the Shannon–Nyquist sampling theorem, a continuous time signal with a bandwidth limited to fm can be recovered from its discrete time samples by an ideal low-pass filter provided that the sampling frequency fs is not less than twice of fm. For example, a continuous time signal with a bandwidth limited to 20 kHz can be recovered from discrete time samples at a sampling frequency of not less than 40 kHz. However, an ideal low-pass filter with a rectangular bandwidth is difficult to be realized. The sampling frequency is usually chosen as 2.1 to 2.5 times of fm to recover the continuous time signal efficiently. A higher sampling frequency is beneficial to reducing the error in the recovered signal. The sampling frequencies commonly used for audio signals are 32, 44.1, 48, 96, and 196 kHz.
Reconstruction of Varying Bandwidth Signals from Event-Triggered Samples
Published in Marek Miskowicz, Event-Based Control and Signal Processing, 2018
Dominik Rzepka, Miroslaw Pawlak, Dariusz Koscielnik, Marek Miśkowicz
The Shannon theorem introduced to engineering community in 1949 is a fundamental result used for digital signal processing of analog signals [1]. The main assumption under which a signal can be reconstructed from its discrete-time representation is that sampling rate is twice higher than the highest frequency component in the signal spectrum (Nyquist frequency), or twice the signal bandwidth. The class of signals with a finite bandwidth is often referred to as bandlimited. The concept of bandwidth is defined using the Fourier transform of the infinitely long signal, that is, the signal that is not vanishing in any finite time interval of (—TO, TO). Furthermore, according to the uncertainty principle, only signals defined over infinite time interval can be exactly bandlimited. As it is known, real physical signals are always time limited, so they cannot be perfectly bandlimited and the bandlimited model is only the convenient approximation [2]. Moreover, in practice, the Nyquist frequency is determined on the basis of the finite record of signal measurements as the frequency for which higher spectral components are weak enough to be neglected. Therefore, the evaluation of the Nyquist frequency is referred not to the global but to the local signal behavior.
On the zero dynamics of linear input–output models
Published in International Journal of Control, 2022
Sneha Sanjeevini, Syed Aseem Ul Islam, Dennis S. Bernstein
In continuous time, the distinction between transfer functions and input–output models resides in the distinction between the Laplace transform variable s and the differentiation operator Analogously, in discrete time, this distinction hinges on the distinction between the Z transform variable z and the forward-shift operator (Middleton & Goodwin, 1990). One consequence of this distinction is the fact that, unlike transfer function models, an input–output model does not require a separate term to represent the free response (Aljanaideh & Bernstein, 2018).
Inner-estimating domains of attraction for discrete-time non-polynomial systems with piecewise difference inclusions
Published in International Journal of Systems Science, 2023
Shijie Wang, Zhikun She, Quanyi Liang, Junjie Lu, Wenyuan Wu
Discrete-time systems are a class of dynamical systems whose state variables take values at discrete time. Note that in some literatures, discrete-time systems are also called as difference systems. In last decades, researches on discrete-time systems have attracted considerable attention since continuous-time systems can be studied with discretization methods, and especially extensive realistic environments exhibit dynamical systems defined by difference equations, such as the difference logistic models, cobweb models in economics, national income models, compound interest models, Boolean control networks, host-parasitoid systems and Markov chain models (Elaydi, 2005).
Lead-time-oriented production control policies in two-machine production lines
Published in IISE Transactions, 2018
Alessio Angius, Marcello Colledani, Andras Horvath
The system is composed of two machines, namely, M1 and M2, and a finite capacity buffer. Finite capacity buffers are used to model the single-stage kanban control policy. Thus, modifying the capacity of the buffer, B, is equivalent to changing the number of kanbans at the production stage. A discrete time system is considered; i.e., time is divided into slots. Both machines have equal and constant processing times. Time is scaled so that the processing cycle of each machine takes one time unit. If operational, machines start their operations at the same time instant. Machine Mi, with i = 1, 2, is unreliable and characterized by Fi failure modes. In particular, machine Mi may fail with probability pi, j whenever it is operational and begins to process a part, where j ∈ {1, …, Fi}. Consequently, for each failure mode, the Times To Failure follow a geometric distribution with mean 1/pi, j. If the machine is down in mode j, it gets repaired in a time slot with probability ri, j. Thus, for each failure mode, the Times To Repair follow a geometric distribution with mean 1/ri, j. For each machine, failure modes are mutually exclusive, in the sense that a machine cannot go down in a certain mode without being repaired from a different failure mode. Therefore, each machine is characterized by a set of states Si with dimensionality Li = Fi + 1, for i = 1, 2. We will denote by U the up state and by Di the ith failure mode. When the machine is operational it processes one part per time unit and it does not process parts if the machine is down. The dynamics of each machine can be captured in the transition probability matrix Ti, which is a square matrix of size Li. An example of a transition probability matrix for a machine with three failure modes is