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An integrator is a device to perform the mathematical operation known as integration
Integral

Integration is an important concept in mathematics, specifically in the field of calculus and, more broadly, mathematical analysis. Given a function ƒ of a Real number variable x and an interval [a, b] of the real line, the integral...
, a fundamental operation in calculus
Calculus

Calculus is a branch of mathematics that includes the study of limit , derivatives, integrals, and infinite series, and constitutes a major part of modern university education....
.

The integration function is often part of engineering
Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
, physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, mechanical
Machine

A machine is any device that uses energy to perform some activity. In common usage, the meaning is that of a device having parts that perform or assist in performing any type of work....
, chemical and scientific
Science

In its broadest sense, science refers to any systematic knowledge or practice. In its more usual restricted sense, science refers to a system of acquiring knowledge based on scientific method, as well as to the organized body of knowledge gained through such research....
 calculations.

Integrator in signal processing
Electronic
Electronics

Electronics refers to the flow of charge through nonmetal electrical conductor , whereas electrical refers to the flow of charge through metal electrical conductor....
 devices have been constructed to perform integration (usually with respect to time) of signals. This operation is a form of first-order low-pass filter
Low-pass filter

A low-pass filter is a electronic filter that passes low-frequency signal but attenuates signals with frequencies higher than the cutoff frequency....
, which can be performed in the continuous-time (analog) domain or approximated (simulated) in the discrete-time (digital) domain.






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Encyclopedia


An integrator is a device to perform the mathematical operation known as integration
Integral

Integration is an important concept in mathematics, specifically in the field of calculus and, more broadly, mathematical analysis. Given a function ƒ of a Real number variable x and an interval [a, b] of the real line, the integral...
, a fundamental operation in calculus
Calculus

Calculus is a branch of mathematics that includes the study of limit , derivatives, integrals, and infinite series, and constitutes a major part of modern university education....
.

The integration function is often part of engineering
Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
, physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, mechanical
Machine

A machine is any device that uses energy to perform some activity. In common usage, the meaning is that of a device having parts that perform or assist in performing any type of work....
, chemical and scientific
Science

In its broadest sense, science refers to any systematic knowledge or practice. In its more usual restricted sense, science refers to a system of acquiring knowledge based on scientific method, as well as to the organized body of knowledge gained through such research....
 calculations.

Integrator in signal processing


Electronic
Electronics

Electronics refers to the flow of charge through nonmetal electrical conductor , whereas electrical refers to the flow of charge through metal electrical conductor....
 devices have been constructed to perform integration (usually with respect to time) of signals. This operation is a form of first-order low-pass filter
Low-pass filter

A low-pass filter is a electronic filter that passes low-frequency signal but attenuates signals with frequencies higher than the cutoff frequency....
, which can be performed in the continuous-time (analog) domain or approximated (simulated) in the discrete-time (digital) domain. An integrator will have a low pass filtering effect but when given an offset it will accumulate a value building it until it reaches a limit of the system or overflows.

See also Integrator at op amp applications
Operational amplifier applications

This article illustrates some typical applications of operational amplifiers. A simplified schematic notation is used, and the reader is reminded that many details such as device selection and power supply connections are not shown....
.

Integrator in computer simulation


In some computational physics
Computational physics

Computational physics is the study and implementation of numerical algorithms in order to solve problems in physics for which a quantitative theory already exists....
 computer simulation
Computer simulation

A computer simulation, a computer model or a computational model is a computer program, or network of computers, that attempts to simulation an abstract model of a particular system....
s, such as numerical weather prediction
Numerical weather prediction

Numerical weather prediction uses current weather conditions as input into mathematical models of the atmosphere to weather forecasting. While the first efforts to accomplish this were done in the 1920's, it wasn't until the advent of the computer that it was feasible to do in real-time....
, molecular dynamics
Molecular dynamics

Molecular dynamics is a form of computer simulation in which atoms and molecules are allowed to interact for a period of time by approximations of known physics,...
, flight simulator
Flight simulator

A flight simulator is a system that tries to copy, or simulation, the experience of flight an aircraft. It is as realistic as possible. The different types of flight simulator range from video games up to full-size cockpit replicas mounted on hydraulic actuators, controlled by state of the art computer technology....
s, reservoir simulation
Reservoir simulation

Reservoir simulation is an area of reservoir engineering in which computer models are used to predict the flow of fluids through porous media....
, noise barrier
Noise barrier

A noise barrier is an exterior structure designed to protect sensitive land uses from noise pollution. Noise barriers are the most effective method of mitigating roadway noise, railway, and industrial noise sources ? other than cessation of the source activity or use of source controls....
 design, architectural acoustics
Architectural acoustics

Architectural acoustics is the science of controlling sound within buildings. The first application of architectural acoustics was in the design of opera houses and then concert halls....
, and electronic circuit simulation
Electronic circuit simulation

Electronic circuit simulation utilizes mathematical models to replicate the behavior of an actual electronic device or circuit. Simulating a circuit?s behavior before actually building it greatly improves efficiency and provides insights into the behavior of electronics circuit designs....
, an integrator is a numerical method for integrating trajectories from forces (and thereby accelerations) that are only calculated at discrete time steps.

There are a variety of explicit and implicit methods
Explicit and implicit methods

In applied mathematics, explicit and implicit methods are approaches used in computer simulations of physics Process , or in other words, they are numerical analysis for solving time-variable ordinary differential equation and partial differential equations....
 used in computer simulations. The most basic and least accurate kind of numerical integration is Euler integration
Euler integration

In mathematics and computational science, the Euler method, named after Leonhard Euler, is a first order numerical analysis procedure for solving Ordinary_differential_equation with a given Initial_value_problem....
. Verlet integration
Verlet integration

Verlet integration is a numerical method used to Time integration method Issac Newton equations of motion. It is frequently used to calculate Trajectory of particles in molecular dynamics simulations and video games....
 improves the accuracy of the integration to within fourth-order Taylor series
Taylor series

In mathematics, the Taylor series is a representation of a function as an Series of terms calculated from the values of its derivatives at a single point....
 terms, and the Runge-Kutta method which is gaining popularity further improves this accuracy to within fifth-order Taylor series terms.

See also

  • Analog computer
    Analog computer

    An analog computer is a form of computer that uses continuous physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved....
  • Digital Differential Analyzer
    Digital Differential Analyzer

    A Digital Differential Analyzer , also sometimes called a Digital Integrating Computer, is a digital implementation of a Differential Analyzer....
  • Fractional order integrator
    Fractional order integrator

    A fractional order integrator or just simply fractional integrator is an integrator device that calculates the fractional order integral or derivative of an input....
  • Lowpass filter
  • Operational amplifier
    Operational amplifier

    An operational amplifier, which is often called an op-amp, is a direct current-Direct coupling high-gain electronic voltage electronic amplifier with differential inputs and, usually, a single output....
  • Planimeter
    Planimeter

    A planimeter is a measuring instrument used to measure the area of an arbitrary two-dimensional shape. The most common use is to measure the area of a plane shape....
  • Signal processing
    Signal processing

    Signal processing is the analysis, interpretation, and manipulation of signal . Signals of interest include: audio signal processing, , time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others....


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