Question

whichof the following i/p-o/p relation describe a time invariant systems​

Answer 1

Answer:

A time-invariant (TIV) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is a function of the time-dependent input function. If this function depends only indirectly on the time-domain (via the input function, for example), then that is a system that would be considered time-invariant. Conversely, any direct dependence on the time-domain of the system function could be considered as a "time-varying system".

Mathematically speaking, "time-invariance" of a system is the following property:[1]:p. 50

Given a system with a time-dependent output function {\displaystyle y(t),}{\displaystyle y(t),} and a time-dependent input function {\displaystyle x(t);}{\displaystyle x(t);} the system will be considered time-invariant if a time-delay on the input {\displaystyle x(t+\delta )}x(t+\delta ) directly equates to a time-delay of the output {\displaystyle y(t+\delta )}y(t+\delta ) function. For example, if time {\displaystyle t}t is "elapsed time", then "time-invariance" implies that the relationship between the input function {\displaystyle x(t)}x(t) and the output function {\displaystyle y(t)}y(t) is constant with respect to time {\displaystyle t}t:

{\displaystyle y(t)=f(x(t),t)=f(x(t)).}{\displaystyle y(t)=f(x(t),t)=f(x(t)).}

In the language of signal processing, this property can be satisfied if the transfer function of the system is not a direct function of time except as expressed by the input and output.

In the context of a system schematic, this property can also be stated as follows:

If a system is time-invariant then the system block commutes with an arbitrary delay.

If a time-invariant system is also linear, it is the subject of linear time-invariant theory (linear time-invariant) with direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas. Nonlinear time-invariant systems lack a comprehensive, governing theory. Discrete time-invariant systems are known as shift-invariant systems. Systems which lack the time-invariant property are studied as time-variant systems

Explanation: