Questions tagged [lti-system]

An LTI system is a Linear Time Invariant system which means the such a system has additive properties and no memory.

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Differential equations of multiple input circuit

I am trying to find the linear differential equation(s) that describe this electrical circuit. When both resistances are equal, I have found the expression: With But how to do it with different ...
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How can I solve this (convolution) integral? [closed]

Let \$x(t) = \sigma(t)\$ where \$\sigma(t)\$ is the unit step function, and \$h(t) = e^{-4t} \cdot \sigma(t)\$. When I try to solve the convolution \$x(t) \ast h(t)\$, I get $$ x(t) \ast h(t) = \...
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What does the real axis of a transfer function mean?

Let's say I have a system that has a transfer function \$ H(s) \$. Now \$ s = \sigma + j \omega \$, so \$ H(s) = H(\sigma + j \omega) \$. If I am not mistaken, the imaginary axis \$ j \omega \$ ...
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Can you automatically know if a system is stable or causal based on its components?

suppose i have system with response Q(s) and I know that the systems H and G are LTI ,BIBO stable and causal. can i automatically say that Q is causal and stable?
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Time invariant system with sinc impulse

Given said system, the impulse responses for the LTI systems \$H_1,H_2\$ are : $$ h_{1}\left(\tau\right)=\frac{\sin\left(\omega_{1}\tau\right)}{\pi\tau}d\tau,h_{2}\left(\tau\right)=\frac{\sin\left(\...
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Confused about the similarities between Fourier Series and Fourier Transform

My understanding of Fourier Series was, it is a method that decomposes a periodic signal into sum of signal given by infinite number of sines and cosines. And in case of Fourier Transform it was, that ...
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Second Order LTI Low Pass Filter solving for Voltage Out

I'm having a problem with understanding my textbook for solving the Voltage Out for the second order LTI Low pass RC Filter. Why do you need to find the square root in the given equation with the red ...
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Second Order Passive Low Pass Filter RC Circuit Design [closed]

I'm learning about Second Order Passive low Pass Filter RC Circuit for my homework. I need to create a circuit with a specification that has a 1 kHz cut off frequency. I quickly learned on how to ...
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Impulse Response of LTI Systems to Dirac Delta

I am reading a book on Linear Time-Invariant systems and came across the following: $$y(t) = T\{x(t)\}$$ where input $$x(t) = \int_{-\infty}^\infty x(\tau)\delta(t-\tau)\text{d}\tau$$ \$\delta\$ is ...
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What does hₖ[n] mean here?

Is the impulse response different from the output y[n]? Is the input x[n] all the delta function at different values of n? From Signals and Systems by Robert Oppenheim, Linear Time Invariant Systems:
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Time invariant system

Is the system \$y(t) = x(t-2) + x(2-t)\$ time invariant? Here is my solution: Let \$x_1(t)\$ be an arbitrary input, then the corresponding output is: \$y_1(t) = x_1(t-2) + x_1(2-t)\$ Let \$x_2(t) = ...
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Finding impulse response by a non-Laplace-transform method

The input function is $$x(t)=e^{-t}u(t)$$ and the corresponding output function of a linear system is $$y(t)=10e^{-t}\cos(4t)u(t)$$ where \$u(t)\$ is unit step function. I understand how to find the ...
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How to plot a pole in the s-plane if it has a repeated root?

Let's suppose I have a transfer function H(s) with a repeated pole: $$H(s) = \frac{1}{(s+2)^2}$$ What would that look like on a pole plot? Do you just circle the -2 on the real number line twice? ...
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Definition of minimal phase

Let us consider a linear time-invariant system. The term minimum phase is used for a system that has stable poles and stable zeros. A system is called nonminimal phase if it is not minimum phase. ...
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Is this system time variant?

I was reading out a book and it said to prove that \$y(t) = sin (t) x(t-2)\$ is time variant, so far of all the inputs I have tried, as well as the general input of giving a shift of T, the system ...
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When did LTI systems become part of the EE curriculum? [closed]

When did universities start teaching the mathematics of LTI systems ("Signals and Systems") as part of the standard curriculum for electrical engineering majors?
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Why non repeated poles at imaginary axis makes LTI system marginally stable?

I understand that stability for an LTI system is defined with respect to Bounded input bounded output condition. However I'm not clear on why non repeated poles on the imaginary axis makes the system ...
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Determining Existence of Transfer Function H(s) and Fourier Transform H(w) for Non-LTI Systems?

Given that $$y(t) = \cos(2\pi t)x(t)$$ where \$x(t)\$ is a system input and \$y(t)\$ is the system's output, I need to determine whether an \$H(s)/H(w)\$ relation exists. Since this system is not LTI, ...
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Is there any correlation between eigen functions and eigen vectors of an LTI system?

Eigen functions are the origin for Laplace transform while eigen vectors is for state space representation.Can we relate the eigen concept in these two? The complex exponential functions, are eigen ...
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Determining whether a system is LTI given response to a rectangle box input

Given a system, it is possible to determine whether the system is LTI given the response to input to the system, other than the unit impulse? Specifically, my input to the system is $$x(t)=\begin{...
Vincent Tjeng's user avatar
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LTI Response Help

A system is known to be LTI. The response of the system to a step function u[n] is δ[n] + δ[n-1]. a.) Find the response of the system to 2u[n] + u[n-1] b.) Find the response to the unit impulse δ[n]....
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