# What is Time invariance: Definition and 24 Discussions

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:
Given a system with a time-dependent output function

y
(
t
)
,

{\displaystyle y(t),}
and a time-dependent input function

x
(
t
)
;

{\displaystyle x(t);}
the system will be considered time-invariant if a time-delay on the input

x
(
t
+
δ
)

{\displaystyle x(t+\delta )}
directly equates to a time-delay of the output

y
(
t
+
δ
)

{\displaystyle y(t+\delta )}
function. For example, if time

t

{\displaystyle t}
is "elapsed time", then "time-invariance" implies that the relationship between the input function

x
(
t
)

{\displaystyle x(t)}
and the output function

y
(
t
)

{\displaystyle y(t)}
is constant with respect to time

t

{\displaystyle t}
:

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.

View More On Wikipedia.org
1. ### A Noether's theorem time invariance -- mean value theorem use?

how does the first step use mean value theorem? I don't get it , can anyone explain , thanks.
2. ### I Time invariance of weak interaciton e-p->\nu n

The question is rather simple, but I cannot seem to find a solid answer. I need the cross section of the following interaction: e^- + p\rightarrow n+ \nu . I need the cross section using the form factors. There are many solutions for the interactions like: n+ \nu\rightarrow e^- + p or...
3. ### Time Invariance of f_n for Quasi-Linear PDE Boundary Conditions

Homework Statement let y(x, t) be a solution to the quasi-linear PDE \frac{\partial y}{\partial t} + y\frac{\partial y}{\partial x} = 0 with the boundary condition y(0, t) = y(1, t) = 0 show that f_n(t) = \int_0^1 y^n\,\mathrm{d}x is time invariant for all n = 1, 2, 3,... Homework EquationsThe...
4. ### Time Invariance of System with x(t) and y(t) Equations

Okay so the question looks like this Determine whether the system with input x(t) and output y(t) defined by each of the following equations is time invariant: (c) y(t) =∫t+1t x(τ−α)dt where α is a constant; (e) y(t) = x(−t); There are more sub-questions but I was able to solve them. The reason...
5. ### I What causes confusion in testing time invariance?

I understand what time invariance means but there are a few catches that I'm completely confused about: Suppose we have $$y(t)=x(\alpha t-\beta)$$ to test time invariance we shift the input then "plug" it into the output:$$x_1(t_1)=x(t-t_o)$$ so this is when I become confused; when we plug...
6. ### I Complex Exponential solutions in time invariant systems

Hi there! First Post :D In a recent CM module we've been looking at coupled oscillators and the role of time translational invariance in the description of such physical systems. I will present the statement that I am having trouble understanding and then continue to elaborate. In stating that...
7. ### Is This System Time Invariant?

Homework Statement y(n)=x(4n+1). Is this system T.I or NOT T.I The professor marked this question wrong for my homework. He says it's NOT time invariant. I proved it is time invariant. Homework Equations System is time invariant if a shift in time in input results in the same shift in time...
8. ### Black holes and time invariance.

Einstein's field equations are time invariant. So is it conceivable that a reverse black hole can exist i.e a "white hole"? Or would the second law of thermodynamics prevent such a thing?
9. ### Time Invariance of a basic system?

Homework Statement I am supposed to determine wether or not the discrete time system x[n] \rightarrow y[n] = x[-n] is time invariant or not. The Attempt at a Solution Let x_d[n] = x[n-n_0] y_d[n] = x_d[-n] = x[-(n-n_0)] = x[-n+n_0] y[n-n_0] = x[-(n-n_0)] = x[-n+n_0] Since y_d[n] =...
10. ### Is the System y(t) = (1/2)(x(t) - x(-t)) Time Invariant?

Homework Statement Prove whether or not, y(t) = \frac{1}{2}\left( x(t) - x(-t) \right) Is time invariant or not Homework Equations The Attempt at a Solution Shifting the output by -T results in, y(t-T) = \frac{1}{2}\left( x(t-T) - x(-(t-T)) \right) y(t-T) = \frac{1}{2}\left( x(t-T) -...
11. ### Determining Time Invariance in Signal Statements: Examples and Solutions

Homework Statement I just have a general question about what one of my professors had written on the board today in class. He was writing down examples where we had to determine whether the given statement was time invariant or not. One example was written as follows, x(-t) = y(t)...
12. ### Causality with time invariance

Assume u:R\rightarrow C^n and define shift operator S(\tau) with S(\tau)u(t)=u(t-\tau) and truncation operator P(\tau) with P(\tau)u(t)=u(t) for t\leq\tau and 0 for t>\tau Then P(\tau)S(\tau)=S(\tau)P(0) for every \tau>=0. Can someone please prove last statement..
13. ### Maxwells Equations and Time Invariance

Hi In my book it says that if the dielectric function ε is time invariant, we can write a solution to Maxwells equations of the form E(r, t) = E(r)exp(jωt). I agree that the ME are separable, but I don't see how they know that the time-dependence is harmonic? What is so special about exp(jωt)...
14. ### Determine if the following system is time invariant: y(t) = x(t - 2) + x(2 - t)

Homework Statement Determine if the following system is time invariant: y(t) = x(t - 2) + x(2 - t) 2. The attempt at a solution I know from the solutions that the system is NOT time invariant, yet whenever I try to solve it I get the opposite result. Here's what I'm doing: y1(t)...
15. ### Proving System is Time Invariant (T.I.) or Not

Homework Statement Prove that the system is either T.I. or is not T.I. Homework Equations y(n) = x(n)*h(n) x(n) is the input signal y(n) is the output signal h(n) is the system The Attempt at a Solution Inputing x(n-n0) into the system I get out: as the output x(n-n0)*h(n)...
16. ### Time invariance of Schrodinger equation

The Schrodinger equation is linear in time. I was wondering if that means that is not invariant under time reversal. That would be a surprise because all other microscopic laws (Maxwell's equations, Newton's equations) are time invariant. Can you please clear this doubt?
17. ### Linearity, time invariance, causality

Homework Statement For each of the following systems, determine whether or not the system is linear, time-invariant, and causal. a) y[n] = x[n]cos(0.2*PI*n) b) y[n] = x[n] - x[n-1] c) y[n] = |x[n]| d) y[n] = Ax[n] + B, where A & B are constants. Homework Equations The Attempt...
18. ### Space and Time Invariance (Classical Wave Equation)

Hey, I've come across a part in my notes which I can't figure out. Essentially it says: \frac{\partial^{2}y}{\partial t^{2}} = v^{2} . \frac{\partial^{2}y}{\partial x^{2}} is space and time invariant. Whereas: \frac{\partial y}{\partial t} = -v . \frac{\partial y}{\partial x} is not...
19. ### Is Proper Time Invariance Proven?

is proper time invariant? proof? thanks...
20. ### Linearity, Time Invariance, Causality, ETC.

Homework Statement Is the following input/output (x is input, y is output) system linear, time invariant, causal, and memoryless? Answer yes or no for each one.Homework Equations y(t)=2x(t)+3The Attempt at a Solution My instinct tells me it's linear, but for some reason I have trouble showing...
21. ### Proving Time Invariance: How to Analyze and Confirm Time Invariance in a System

Homework Statement Show that y(t) = \frac{d}{dt}\left[e^{-t}x(t)\right] is time invariant. 2. Relevant Information I don't think this is TI! I'm told it is TI, but I think I proved that it is not TI! My proof is below. Am I wrong or is the question wrong in assuming that the...
22. ### Checking for time invariance

Homework Statement Consider the following input-output relationship: y(t) = \int_0^\infty e^{-\sigma}x(t-\sigma) d\sigma A) Is the system time-invariant? B) Find the output y(t) when the input to the system is x(t) = \mid t \mid , -\infty < t < \infty Homework Equations These are the...
23. ### Understanding Time Invariance in Signals

i usually have such a hard time determining whether a signal is time invariant or not ... for example, why would x[-n] not be time-invariant? please don't just tell me why x[-n] would not be time invariant ... tell me techniques that I can apply to other signals too
24. ### Noether's theorem and Time invariance?

Hi, I know I'm probably going to get shot down in flames. I'm a total amateur to all of this. But I do try to read things and I do try to understand them - so I hope you guys will at least be patient with me. But in any case I have been reading around about Noether's theorem and about the...