The concept of signal arises in a wide variety of fields of science and technology as in communication, circuit design, seismology, bio medical engineering and speech processing etc. In simple terms anything that carries some sort of information is known as a signal.When a signal is given as input to a compatible system for required modifications then what we get as a result is known as an output signal. Signals and Systems together forms the basis for the subject known as digital signal processing. Here in this article we are going to discuss Classification of Signals as causal, anti causal and non-causal signals in form of Signals and Systems Notes in detail.
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Classification of Signals:
1) Continuous-time and Discrete-time Signal.
2) Periodic and Aperiodic Signals.
3) Causal, Anti-Causal and Non-Causal Signal
4) Deterministic and Random Signal.
Causal Signals are signals that are zero for all negative time. Causality in systems makes the most sense. Causality in signals doesn’t make that much sense. Causality in a systems determines whether a system relies on future information of a signal x[n+1]. When talking about “causality” in signals, we mean whether they are zero to the left of t=0 or zero to the right of t=0.
A causal signal is zero for t<0. However, the reason why this doesn’t really make sense is that if you have a signal, the time t=0 can be chosen arbitrarily.
A continuous time signal x(t), is said to be casual if : x(t)=0 for every t<0, the signal x(t) does not start before t=0.
Non Causal Signals:
Non-causal means that the response of the system needs to start before the excitation. For example, if you add an impulse to the input at a certain time T, a normal (causal) system will start responding from time T, T+1, T+2,…..
A non-causal system would start its response before the input, e.g. T-10, T-9, … T, T+1, …
This is of course not a natural system because it would need to predict the future and start responding before the input.
A continuous time signal x(t), is said to be non-casual if : x(t)=0 for every t>0, the signal x(t) start before t=0.
Anti Causal Signals:
An anti-causal system is a signal with outputs and internal states that depend solely on future input values. Some textbooks and published research literature might define an anti-causal system to be one that does not depend on past input values (i.e. its outputs and internal states depend only on future and possibly present input values).
An anti causal system is a system that is not a causal signal 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.
Anti-causal systems are also anti-causal, but the converse is not always true. An anti-causal system that has any dependence on past input values is not anti-causal.
For Example: Anti causal signal processing is the production of an output signal that is processed from another input signal that is recorded by looking at input values both forward and backward in time from a predefined time arbitrarily denoted as the “present” time. (In reality, that “present” time input, as well as the “future” time input values, have been recorded at some time in the past, but conceptually it can be called the “present” or “future” input values in this anti-causal process.)
This type of processing cannot be done in real time as future input values are not yet known, but is done after the input signal has been recorded and is post-processed.
Condition for causal anti causal and non causal are as follows:
Condition for Causal Signal: A signal which posses zero amplitude for all negative value of time, then the signal is known as a causal signal.
X(t) > 0 , for t >= 0 &
X(t)=0 , for t<0.
Condition for Non-Causal Signal: A signal that has positive values of amplitude for both positive and negative instances of time is a non-causal signal.
Condition for Anti-Causal Signal: A signal which posses zero value for all positive value of time, but has amplitude which is greater then zero for all negative value of time, then the signal is known as anti-causal signal.
X(t) > 0 , for t <= 0 &
X(t)=0 , for t>0.
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