# What is Lti: Definition and 47 Discussions

LTI – Lingua Tertii Imperii: Notizbuch eines Philologen (1947) is a book by Victor Klemperer, Professor of Literature at the Dresden University of Technology. The title, half in Latin and half in German, translates to "The Language of the Third Reich: A Philologist's Notebook"; the book is published in English translation as The Language of the Third Reich.

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1. ### I On the stability of an LTI circuit

An LTI circuit such as one composed of resistors, capacitors, and inductors, in general is a stable LTI system, i.e. its impulse response is one that decays over time. I have no problem with that, as it speaks for itself through laws of energy conservation, but I want to see this from a...
2. ### Output of an LTI system when the input is multiplied with 'n'

Homework Statement Homework Equations Find out the function of the system. Apply that to input. The Attempt at a Solution From given input output, system is a differentiator. So when input is n u[n] output is differentiating it, we get: n (impulse response) + u[n] Which is not in any of the...
3. ### A $L^2(-\infty, +\infty)$ and LTI systems

Hi everyone, I'm an electrical engineer trying to make a little bit of order in my mind about eigenfunction theory, sturm liouville operators (regular and singular) on my own free time and I thought I was grasping almost everything, but I had a little doubt that is actually coming from the field...
4. ### Response of LTI discrete time causal system

Homework Statement Discrete time causal LTI system has impulse response h(n) = (-1/2)^n, n≥0. a)Find transfer function of given system. b)Find frequency characteristics of system. c) Find response for u(n) = μ(n)-μ(n-4) The Attempt at a Solution a) Either from definition, or from table...
5. ### A LTI Impulse Response Estimation with Point Process Input

Hello, I am trying to estimate transfer function of unknown LTI system, given output and assumed input as point process. I have measurement of output, while input, which is assumed to be point process, could be created synthetically using known times and amplitudes. My questions: 1. What is...
6. ### Question about an LTI System and its Frequency Response

Hello All, I am trying to learn about lti systems and what not for my research work but before I can apply my research I have to understand the fundamentals, which is what this question is kind of about! I want to find h(t), the impulse response of an LTI system where my input and output are...
7. ### Finding the closed form of a recursive LTI system

Homework Statement Find the closed form of the impulse response of the system y[n] = 7y[n-1]-12y[n-2]+x[n] using the peel away and guess method. Ie, by using Python code to find the geometric ratios and amplitudes of the outputs as n grows large, then calculate residuals, and find the...
8. ### 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...
9. ### Find the Output of an LTI System Given Input and Impulse Response

Homework Statement Consider a LTI system for which the filter coefficients are ##{\mathrm{h}_k}=\{1,2,1\}##. Find the output when the input is ##\mathrm{x}[n]=3\mathrm{cos}(\frac{\pi}{3}n-\frac{\pi}{2})-3\mathrm{cos}(\frac{7\pi}{8}n)##. Identify two frequencies in this composite signal. Show...
10. ### Help proving if a system is LTI?

Homework Statement A DT system is defined by the input-output relationship y[n] = x[n] ∗ h[n], where x[n] is input, y[n] is output, '*' is convolution, and h[n] = u[n+1]. Is this an LTI system? Explain. Homework Equations x[n] - input, h[n] - impulse response y[n]=h[n]*x[n] = Σ (k=-inf to inf)...
11. ### How do I solve this LTI acceleration sensor problem?

Homework Statement Please see he attached file for the problem text. Homework Equations The output ##y(t) = h(t) * x(t)##, where ##h(t)## is the system's impulse response while ##x(t)## is the input signal. Laplace transformed, the formula above turns into ## Y(s)=H(s) \cdot X(s)##, where...
12. ### Why is convolution used to represent LTI output?

Hi. If you have a LTI system with an impulse response function ##h(t)## taking in an input ##x(t)##, why does its output ##y(t)## become ? I realize ##y(t)## not only depends on the instantaneous input ##x(t)##, but also on the lingering effects of previous inputs ##x(\tau)## with ##\tau <...
13. ### LTI Systems, Delta Distribution, and more

Hi, For my math methods 3 course, I am not quite sure which books to use. The course is based on the math methods book by Riley, Hobson, and Bence, and I don't particularly like it. Hence, I am looking for some alternatives. Especially for the Preliminaries section. I had a real hard time...
14. ### Linear system - calculate output signal

Hi! Homework Statement a) Calculate and sketch amplitude spectrum of u(t), b) u(t) is input signal for linear time invariant system whose transfer function H(jw) is shown. Calculate output signal uo(t) Homework EquationsThe Attempt at a Solution I completed task a), I got...
15. ### Finding LTI (Linear Time-Invariant Systems)

Homework Statement Tell whether following systems are i. linear and ii. time-invariant: $$y(t) = \int_{-\infty}^t x(\tau)d\tau$$ $$y(t) = \int_{0}^t x(\tau)d\tau$$ $$y(t) = \int_{t-1}^{t+1} x(\tau)d\tau$$Homework Equations N/AThe Attempt at a Solution I'm a little thrown off by the integrals...
16. ### Finding Pole-zero pattern of transfer fcn and Stability of LTI system

Homework Statement The transfer function of an LTI system H(s) = (s^2 + 2)/(s^3+2s^2+2s+1) Find the followings i) pole-zero pattern of H(s) ii) Stability of the system iii) Impulse response h(t) Homework Equations Zero for which H(s) = 0 & Pole is for which H(s) = ∞ The...
17. ### MHB Find $$H(s)$$ for Causal LTI System: Region of Convergence

Determine $$H(s)$$ and specify its region of convergence. Your answer should be consistent with the fact that the system is causal and stable. In order to find $$H(s)$$, we need to find $$X(s)$$ and $$Y(s)$$. \begin{align*}...
18. ### LTI system and sinusoids/complex exponentials

Not sure if this is the right forum. This is a mathematical question, but it is from signals. An LTI system is a mapping from one function space to another that is both linear and time invariant. Given this, how might I show that if the input is a sinusoid, the output, is also a sinusoid...
19. ### LTI systems- frequency response

I have attached an image of a ''brick-wall'' band pass filter. Can someone please help me find the expression of frequency response for it? Homework Statement Homework Equations The Attempt at a Solution
20. ### How Do LTI Systems Use Convolution to Compute Outputs?

How would you interpretate this image about LTI systems and convolution?
21. ### Determine the unit-step response of the discrete-time LTI systems

Determine the unit-step response of the discrete-time LTI systems described by the following impulse responses: h[n]=(0.9)^{n}e^{j(\pi/2)n}u[n]So I am completely confused. . . I don't even know how to start. . . I want to say that I need to do a summation but the more examples and text I look...
22. ### Quick question about Causal LTI system

Homework Statement I am reading a little bit on Causal LTI systems. I know causality means that a system cannot depend on the future, but why does that mean an impulse function, say h(t) = 0, for all t<0 I mean, if t is negative, then it's not really depending on the future, but the...
23. ### Find Impulse Response of LTI system given transfer function

Homework Statement Find the impulse response of a system with transfer function H(S) = (s+3)/(s^2+2s+1) or H(S)=(s+3)/[(s+1)^2] Homework Equations Poles are s1=s2=-1 y = Ae^st + Be^st The Attempt at a Solution In my notes I do not have an answer for the case when there is...
24. ### Continuous Time Fourier in LTI system

Homework Statement Homework Equations Not sure The Attempt at a Solution No idea how to even begin. I don't even know how to start this equation. My textbook has no examples of this type. Do I need to transform x(t)? If someone could simply steer me in the right direction...
25. ### Proving a system is LTI based on input and output

edit: you aren't proving it's LTI, you proving it COULD be lti Homework Statement the question: could the following system be LTI? x(t)=-5cos(2t) --> y(t)=exp(-2tj)Homework Equations the chapter is about eigenfunctions of LTI systems, which are of the form exp(st).The Attempt at a Solution So...
26. ### Obtaining Impulse Response & Frequency Response of LTI System

Homework Statement An LTI discrete-time system has frequency response given by (a) Use one of the above forms of the frequency response to obtain an equation for the impulse response h[n] of the system. (b) From the frequency response, determine the difference equation that is...
27. ### Statistics of random processes passed through an LTI system

Hello, I apologize in advance if I have missed the right place to ask. I'd be grateful if you could forward me to the right place, if that is the case. Google didn't help, so maybe someone here can point me in the right direction: 1) "If the input to a LTI system is a Gaussian random...
28. ### LTI Difference Equation from Impulse response

I've been told that to calculate the difference equation of an LTI system, you simply take the sample values of the impulse response as the coefficients of the x[n-k] terms in the difference equation. i.e. if h[n] = {1, 0.5, 0.25, 0.125} for n>=0, then y[n] = x[n]...
29. ### To determine whether it's LTI system

Homework Statement this system satisfies the condition of initial rest. Y[n] =(1/2)y[n-1] + x[n] I'm trying to prove that this is linear and time invariant.The Attempt at a Solution I'm trying it this way. To be LTI system, It has to satisfy below. aX1[n] -> aY1[n] bX2[n] -> bY2[n] aX1 +...
30. ### How Does Normality Arise in the Output of an LTI System with Normal Noise Input?

Homework Statement The signal s(t) is a deterministic signal with the finite duration (0,Ts) and the energy Es=∫s2(t)dt. In the following system, n(t) is a normal noise with the mean zero and the power spectral density Gn(f)=η/2. Show that no(Ts) has a normal distribution with the mean zero...
31. ### How Do You Calculate the Step Response of an LTI System?

Homework Statement Calculate the step response of the system (i.e. response to x(n) = u(n) Previously calculated the impulse response becomes h(n) 3/11 (5/8)^{n} u(n) + 5/22(1/8)^{n}u(n) Homework Equations H(z) =\frac{Y(z)}{X(z)} u(n) =\frac{1}{1-z^{-1}} The Attempt at a...
32. ### Deriving the Group Delay of an LTI Discrete-Time System

Homework Statement Show that the group delay of an LTI discrete-time system characterized by a frequency response H(e^{j\omega}) can be expressed as \tau(\omega)= Re\left\{\frac{j\frac{dH(e^{j\omega}}{d\omega}}{H(e^{j\omega}}\right\} . Homework Equations The...
33. ### Understanding an Exercise on LTI Systems with Unit Sample Response

Hello, am having an understanding problem, about an exercice on LTI systems with unit sample response. i've been given the graphical depicted output y[n], and the following output x[n]= u[n]-u[n-2] the system is as follow x[n]----> h1[n]----->h2[n]------>y[n] with h2[n]= s[n] - s[n-1]...
34. ### State space representations in LTI systems

I just started my first graduate level controls class this semester, and it looks like my professors notes aren't going to be quite enough. Can anybody recommend a good book with lots of state space representation examples, or if not a book, a website would do fine as well. Thanks for any help.
35. ### Finding the output of an LTI system when we know the system function

Homework Statement Suppose that we have a linear time invariant system with a system function H(s) = \frac{s+1}{s^{2} + 2s + 2} we want to find the output of the system when the input is x(t) = e^{\left | t \right |} The Attempt at a Solution what I tried to do is find the laplace...
36. ### Representing Fourier Transform of Periodic Signal in LTI System

How do you represent the Fourier transform of a periodic signal as the input in a LTI system? More precisely, a sequence of triangle pulses symmetric to the origin. I know what the Fourier transform is 2\pi (sum (Xn delta(omega - (n)omega0))) I was told to reduce the Xn to...
37. ### How Can I Determine the Equivalent Transfer Function of Two Active LTI Systems?

hello, If I have two LTI system in G1(s) and G2(s) and I know that for a certain fraction of the time period G1 is active and for the reminaing fraction G2 is active, then is there any method to get the equivalent transfer function ? Umat.
38. ### Is System Stability of LTI System Proven?

Is the following system stable. If so how. y(t)= \frac{d}{dt} x(t)I have tried the following proof but i think it is wrong. PROOF: The System is LINEAR The system is time invariant So on applying the stability criterion for LTI systems ie . \int^{\infty}_{-\infty} h(t) dt < \infty...
39. ### Find Out if System is LTI - Input & Output Analysis

how to find whether the system is LTI or not when only its input and output is given . . .
40. ### Discrete LTI filter impulse response

If I have the unit impulse response function for a discrete-time LTI system (Unit sequence response?), h[n], how can I calculate the time taken for the output to fall below 1% of its initial value, after a unit impulse is applied to the input? In particular, I have: h[n]=(\alpha...
41. ### Step Response of an LTI system

Hi lads, need help with this question from a signals and systems course. LTI system is defined as follows H(s) = \frac{1}{ s^2 - 2rs cos(theta) + r^2} where r = 20pi, theta = 1.47. Find an expression for the step response of the system I think...
42. ### Limit of u(t)- u(t -\delta) as delta goes to zero, LTI systems

Homework Statement what is the limit of yb(t) as \delta goes to zero. yb(t) = (b/delta)*exp[-t/RC](exp[delta/RC] - 1)(u(t)-u(t-delta)) b=1. 2. The attempt at a solution I used L'hopitals rule to find the limit of (b/delta)*exp[-t/RC](exp[delta/RC] - 1), which i got to...
43. ### Problem inverting Z transform for DT LTI system

Homework Statement Hello all, As part of a Control Theory assignment I have to compute the step response for the discrete-time LTI system given by the following state-space matrices: A = $\left( \begin{array}{ccc} 0 & 1 \\ 0 & 3 \end{array} \right)$ B = \[ \left(...
44. ### Reciprocity theorem and LTI systems

I am looking for good, theoretical references on the reciprocity theorem for resistor networks. I am trying to find out how general the theorem is and whether it is only limited to LTI systems. Thanks in advance for the suggestions...
45. ### Causality Condition(Continuous time LTI systems)

Can anybody prove or give a bit detail about the causality condition i.e h(t) = 0, t<0 for continuous-time LTI system. And based on this how a continuous time LTI system is causal if, x(t) = 0, t<0.
46. ### Exponentials as eigenfunctions in LTI Systems

I hope I catched the correct forum. Under http://en.wikipedia.org/wiki/LTI_system_theory e^{s t} is an eigenvalue. I don't really understand that the following is an eigenvalue equation: \quad = e^{s t} \int_{-\infty}^{\infty} h(\tau) \, e^{-s \tau} \, d \tau \quad = e^{s t}...
47. ### Signals and Systems: Response of LTI systems to Complex Exponentials

How will we evaluate the integral for calculation of Amplitude Factor for an LTI system for which the input and output are related by a time shift of 3, i.e., y(t) = x(t - 3) The answer is: H(s) = e^(-3s) I want to understand the Mathematics behind the evaluation of the integral...