Acausal System
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Acausal System
In systems theory, an anticausal system is a hypothetical system with outputs and internal states that depend ''solely'' on future input values. Some textbooks and published research literature might define an anticausal system to be one that does not depend on past input values, allowing also for the dependence on present input values. An acausal system is a system that is not a causal system, that is one that depends on some future input values and possibly on some input values from the past or present. This is in contrast to a causal system which depends only on current and/or past input values.Distinguishing Causal and Acausal Temporal Relations, Kamran Karimi and Howard J. Hamilton, The seventh Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), 2003. This is often a topic of control theory and digital signal processing (DSP). Anticausal systems are also acausal, but the converse is not always true. An acausal system that has any dependence on pas ...
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Systems Theory
Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems. A system is "more than the sum of its parts" by expressing synergy or emergent behavior. Changing one component of a system may affect other components or the whole system. It may be possible to predict these changes in patterns of behavior. For systems that learn and adapt, the growth and the degree of adaptation depend upon how well the system is engaged with its environment and other contexts influencing its organization. Some systems support other systems, maintaining the other system to prevent failure. The goals of systems theory are to model a system's dynamics, constraints, conditions, and relations; and to elucidate principles (such as purpose, measure ...
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System
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, structure and purpose and expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term ''system'' comes from the Latin word ''systēma'', in turn from Greek language, Greek ''systēma'': "whole concept made of several parts or members, system", literary "composition"."σύστημα"
Henry George Liddell, Robert Scott, ''A Greek–English Lexicon'', on Per ...
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Causal System
In control theory, a causal system (also known as a physical or nonanticipative system) is a system where the output depends on past and current inputs but not future inputs—i.e., the output y(t_) depends only on the input x(t) for values of t \le t_. The idea that the output of a function at any time depends only on past and present values of input is defined by the property commonly referred to as causality. A system that has ''some'' dependence on input values from the future (in addition to possible dependence on past or current input values) is termed a non-causal or acausal system, and a system that depends ''solely'' on future input values is an anticausal system. Note that some authors have defined an anticausal system as one that depends solely on future ''and present'' input values or, more simply, as a system that does not depend on past input values. Classically, nature or physical reality has been considered to be a causal system. Physics involving special relat ...
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Control Theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system eng ...
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Digital Signal Processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor. Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. DSP can involve linear or nonli ...
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Real-time Computing
Real-time computing (RTC) is the computer science term for hardware and software systems subject to a "real-time constraint", for example from event to system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines". Ben-Ari, Mordechai; "Principles of Concurrent and Distributed Programming", ch. 16, Prentice Hall, 1990, , page 164 Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds. A system not specified as operating in real time cannot usually ''guarantee'' a response within any timeframe, although ''typical'' or ''expected'' response times may be given. Real-time processing ''fails'' if not completed within a specified deadline relative to an event; deadlines must always be met, regardless of system load. A real-time system has been described as one which "controls an environment by receiving data, processing them, and returning the results sufficiently quic ...
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Digital Room Correction
Digital room correction (or DRC) is a process in the field of acoustics where digital filters designed to ameliorate unfavorable effects of a room's acoustics are applied to the input of a sound reproduction system. Modern room correction systems produce substantial improvements in the time domain and frequency domain response of the sound reproduction system. History The use of analog filters, such as equalizers, to normalize the frequency response of a playback system has a long history; however, analog filters are very limited in their ability to correct the distortion found in many rooms. Although digital implementations of the equalizers have been available for some time, digital room correction is usually used to refer to the construction of filters which attempt to invert the impulse response of the room and playback system, at least in part. Digital correction systems are able to use acausal filters, and are able to operate with optimal time resolution, optimal fr ...
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Sound Recording And Reproduction
Sound recording and reproduction is the electrical, mechanical, electronic, or digital inscription and re-creation of sound waves, such as spoken voice, singing, instrumental music, or sound effects. The two main classes of sound recording technology are analog recording and digital recording. Sound recording is the transcription of invisible vibrations in air onto a storage medium such as a phonograph disc. The process is reversed in sound reproduction, and the variations stored on the medium are transformed back into sound waves. Acoustic analog recording is achieved by a microphone diaphragm that senses changes in atmospheric pressure caused by acoustic sound waves and records them as a mechanical representation of the sound waves on a medium such as a phonograph record (in which a stylus cuts grooves on a record). In magnetic tape recording, the sound waves vibrate the microphone diaphragm and are converted into a varying electric current, which is then converted to ...
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Anti-causal Filter
In signal processing, a causal filter is a linear and time-invariant causal system. The word ''causal'' indicates that the filter output depends only on past and present inputs. A filter whose output also depends on future inputs is non-causal, whereas a filter whose output depends ''only'' on future inputs is anti-causal. Systems (including filters) that are ''realizable'' (i.e. that operate in real time) must be causal because such systems cannot act on a future input. In effect that means the output sample that best represents the input at time t, comes out slightly later. A common design practice for digital filters is to create a realizable filter by shortening and/or time-shifting a non-causal impulse response. If shortening is necessary, it is often accomplished as the product of the impulse-response with a window function. An example of an anti-causal filter is a maximum phase filter, which can be defined as a stable, anti-causal filter whose inverse is also stable and ...
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Control Theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system eng ...
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Digital Signal Processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor. Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. DSP can involve linear or nonli ...
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