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Causal and Noncausal System(Causality Property)

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Causal and Noncausal System:

A) Causal systems:

Definition:

A system is said to be causal system if its output depends on present and past inputs only andnot on future inputs.

Examples:

The output of casual system depends on present and past inputs, it means y(n) is a function ofx(n), x(n-1), x(n-2), x(n-3)…etc. Some examples of causal systems are given below:

1) y(n) = x(n) + x(n-2)

2) y(n) = x(n-1) – x(n-3)

3) y(n) = 7x(n-5)

Significance of causal systems:

Since causal system does not include future input samples; such system is practicallyrealizable. That mean such system can be implemented practically. Generally all real timesystems are causal systems; because in real time applications only present and past samples arepresent.

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Since future samples are not present; causal system is memoryless system.

B) Anticausal or non-causal system:

Definition:

A system whose present response depends on future values of the inputs is called as a non-causal system.

Examples:

In this case, output y(n) is function of x(n), x(n-1), x(n-2)…etc. as well as it is function of x(n+1),x(n+2), x(n+3), … etc. following are some examples of non-causal systems:

1) Y(n) = x(n) + x(n+1)

2) Y(n) = 7x(n+2)

3) Y(n) = x(n) + 9x(n+5)

Significance:

Since non-causal system contains future samples; a non-causal system is practically notrealizable. That means in practical cases it is not possible to implement a non-causal system.

But if the signals are stored in the memory and at a later time they are used by a systemthen such signals are treated as advanced or future signal. Because such signals are alreadypresent, before the system has started its operation. In such cases it is possible to implementa non-causal system.Some practical examples of non-causal systems are as follows:

1) Population growth

2) Weather forecasting

3) Planning commission etc.

For continuous time (C.T.) system:

A C.T. system is said to be “causal” if it produces a response y(t) only after the application ofexcitation x(t). That means for a causal system the response does not begin before theapplication of the input x(t).

The other way of defining the causal system is as follows:

A system is said to be “causal” if its output depends on present and past values of the input

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A system is said to be “causal” if its output depends on present and past values of the inputand not on the future inputs. If the input is applied at t = tm then the output at t = tm y(tm) willbe dependent only on the values of x(t) for t ≤ tm.

Condition for causality: y(tm) = f[x(t); t ≤ tm]

Causal systems are physically realizable systems. The non-causal systems do not satisfy abovecondition. Non-causal systems are not physically realizable.

Condition for causality in terms of impulse response h(t):

The relation between y(t) and x(t) is given by,

y(t) = x(t)*h(t)

Where * represents convolution and h(t) is the impulse response of the system. The conditionfor causality in terms of the impulse response is as follows:

Condition for causality: h(t) = 0 for t<0

This condition states that a linear time invariant (LTI) system is “causal” if its impulse responseh(t) has a zero value for negative values of time.

Solved problems:

Determine if the systems described by the following equations are causal or non-causal.

1) y(n) = x(n) + x(n-3)

Solution: the given system is causal because its output (y(n)) depends only on the present x(n)and past x(n-3) inputs.

2) y(n) = x(-n+2)

Solution: this is non-causal system. This is because at n = -1 we get

y(-1) = x[-(-1)+2] = x(3).

Thus present output at n = -1, expects future input i.e. x(3)

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Tags: Causality (http://myclassbook.wordpress.com/tag/causality/), CLASSIFICATION(http://myclassbook.wordpress.com/tag/classification/), dynamic(http://myclassbook.wordpress.com/tag/dynamic/), invarient(http://myclassbook.wordpress.com/tag/invarient/), Linearity(http://myclassbook.wordpress.com/tag/linearity/), properties(http://myclassbook.wordpress.com/tag/properties/), Stability(http://myclassbook.wordpress.com/tag/stability/), static(http://myclassbook.wordpress.com/tag/static/), system(http://myclassbook.wordpress.com/tag/system/), time(http://myclassbook.wordpress.com/tag/time/), varient(http://myclassbook.wordpress.com/tag/varient/)

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CATEGORIES Signals and Systems

3 Responses to “Causal and Noncausal System(Causality Property)”

Pico August 4, 2013 at 7:21 PM #

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I appreciate your effort in putting these materials in the webpage,but I would like to pointout a mistake.Anti Causal systems do not depend on past .Non causall depends on past,anti causalstrictly depends on present and future

Pico

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REPLYMayuresh Joshi August 4, 2013 at 8:36 PM #

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Thanks for showing your interest in my post. (i am totally appreciate with you) i havecorrected a definition of anticausal system.once again thanks for correcting my post. Stay connected.

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REPLYhagos April 9, 2014 at 6:54 PM #

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and also i add ,a signal that is zero for -ve time are causal signals while anticausal signals are zerofor all +ve/positive time .But for signals that have non zero in both negative andpositive are non-causal signals.

thanks

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