Time invariance Definition and 22 Threads

how does the first step use mean value theorem? I don't get it , can anyone explain , thanks.

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...

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...

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...

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...

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...

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?

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] =...

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)...

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..

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)...

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)...

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)...

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?

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...

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...

is proper time invariant? proof? thanks...

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...

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...

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...

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

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...