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Two meanings for "innovation" in Wiener filter are the same?

This is related question to A question about Wiener filter based on Linear Estimation by Kailath, based on the textbook Linear Estimation by Kailath. In that link I talk about how I first learned what ...
monad's user avatar
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21 views

A question about Wiener filter based on Linear Estimation by Kailath

In my linear estimation class based on the textbook Linear Estimation by Kailath, we went through the process of finding LLSE of $\hat{x}(t+\lambda)$ for fixed $\lambda$ given $\{y(\tau)|-\infty<\...
monad's user avatar
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83 views

Impulse response of a causal LTI system without using Laplace transform

I have this differential equation that models a causal LTI system: $$ \ddot{v}(t) - \dot{v}(t) - 2v(t) = \ddot{u}(t) + 2\dot{u}(t) + u(t) $$ I was asked to find the impulse response both by using ...
Lorenzo's user avatar
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1 answer
18 views

How to compute the 2D coordinate in the s-domain?

I am not sure if my question is a right question to ask or not since I am still learning about Laplace Transform and S-Domain. If we have 2D coordinates (x,y) in the spatial domain (i.e., Euclidean ...
S.EB's user avatar
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Laplace Transform and Inverse laplace Transform for 2D images python code available?

I am wondering if there is any implementation of Laplace Transform and Inverse Laplace Transform available for 2D data (i.e., images). For example, a batch of N ...
S.EB's user avatar
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1 answer
214 views

Are complex exponentials real thing?

Is there any physical significance of complex exponentials. I mean can we produce them like how we can produce sinusoidal signals using a signal generator? OR are they just pure mathematical ...
amoghfyi's user avatar
1 vote
1 answer
90 views

Why do singularities on the imaginary axis affect the Fourier transform differently than the Laplace transform?

(Please note that I'm aware there are already several questions asking about the difference between the two transforms. However, none of them that I could find touch on this specific issue of the ...
Mikayla Eckel Cifrese's user avatar
2 votes
2 answers
133 views

Laplace transform of this simple parallel RLC circuit? (For audio speaker simulation ...)

SPEAKER AS RLC CIRCUIT I read this article here which demonstrates a simulation of a speaker as a simple RLC circuit where the RLC components are in parallel: MY GOAL I am interested in creating a ...
mike's user avatar
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50 views

Bode plot phase shift equation when poles and zeros are not at the origin

Let $$H(s)=\frac{s^{n}}{s^{m}}$$ For $n \ne m$ the phase shift between output and input will be $\frac{\pi}{2}(n-m)$. For situations where the poles and zeros are not at the origin, I could find the ...
Cerise's user avatar
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61 views

Mixer and control systems

A mixer in the time domain usually multiplies 2 signals of the time domain , however what does it do in the Laplace domain?Is there a equivalent block diagram of a mixer in the Laplace domain?The ...
Cerise's user avatar
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Simulate Op-Amp low-pass transfer function in Python

I am struggling to simulate the frequency response of a simple op-amp low-pass transfer function in Python. The results I get are not accurate. The transfer function is $H(s)=\frac{1}{1 + s\tau}$, ...
MisterFilter's user avatar
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109 views

I have a transfer function in s domain convert to time domain

I have a transfer function of $\frac{1}{s^2}$ in $s$ domain that represents a $\frac{\text{output}(s)}{\text{input}(s)}$. Say I put a constant DC input as input (s) or just input in time domain that ...
user43423432432's user avatar
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73 views

Equipment to test my theory on time varying systems

How can I make a linearly time varying system to test my theory? Can I ask for a PID microcontroller available from my university such that $K$ is gradually increased from 0 to $c$
Volpina's user avatar
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105 views

Correlation gives contradictory results

I am trying to find the correlation between the signals $u(t)$ and $\sin(t)[u(t)-u(t-2)]$ The correlation function $C(t) = \int^{\infty}_{-\infty} u(\tau+t)\sin(t)(u(t)-u(t-2))d\tau$ This is my ...
Cerise's user avatar
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82 views

Derivation of 9 point Laplacian filter

I'm reading a paper on how construct isotropic laplacian filter, and perhaps because it's an old paper, the notation in it really bothers me a lot. So can someone please explain it to me? For example, ...
Ili a's user avatar
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1 answer
84 views

Is there a Fourier Transform generalization that lets you analyze arbitrary complex frequencies?

Suppose you have a function that can be described as $$f(s) = \sum_{n=0}^{\infty} a_n e^{f_n s}$$ where each $f_n$ is a complex number. I am looking for a transform $T$ to act on $f$ which produces a ...
Sidharth Ghoshal's user avatar
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3 answers
113 views

How to separate Transient and Steady-State Expression from Periodic Summation Response?

Background My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input. How to determine the transient response of a circuit to causal periodic inputs? ...
Unknown123's user avatar
1 vote
1 answer
241 views

Laplace domain transfer function from system sampled at discrete times

I'm trying to understand an analysis of a sampled continuous time system in the Laplace domain. The source analysis is here (PDF page 6, slide marked 11); I'll explain further below. Suppose I have a ...
Halleff's user avatar
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1 answer
135 views

Finding the region of stability of a system

Suppose we have a closed loop system controlled by some microcontroller $K$ First we take the open loop gain which is $\frac{K}{s(s+6)}$.It has 1 pole at the origin and at $s=6$ and 0 zeros. So we ...
Volpina's user avatar
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2 answers
435 views

Calculating transfer function of a linear time varying system?

If we excite a LTI system with the Dirac delta $\delta(t)$, the system outputs the impulse response $h(t)$. For a LTI system, it doesn't matter when we excite the system with the Dirac delta, we will ...
Volpina's user avatar
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1 answer
37 views

Max input of a system given it's transfer function and an assumed step change (beginner)

I have an exercise that gives me the following transfer function $$ \frac{0.5}{s+0.5} $$ and an assumed step change in the target of 20 I am asked to calculate the maximum input for the assumed step ...
Tom Callan's user avatar
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62 views

LLTV Systems breakdown(2)

In this question I proved that for a linear linearly time varying system $S$ such that if $t_{2} = t_{1}+t_{0}$ then $h(t,t_{2}) = h(t,t_{1})+h(t,t_{0})\rightarrow$ $h(t,t_{0}) = g(t_{0})h(t) $ where $...
Volpina's user avatar
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235 views

What exactly are the assumptions behind Tustin's formula? Application on state space models

I was parsing the forum when I saw this post surging out of the depths of this forum like an old Kraken. The problem is quite simple. You have a continuous time state space model : $$ \begin{split} \...
NokiYola's user avatar
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0 answers
73 views

Linear linearly time varying systems Laplace transform

Suppose that for a system $S$ if we have $t_{2} = t_{1}+t_{0}\rightarrow h(t,t_{2}) =h(t,t_{1})+h(t,t_{0}) $ .Then if we take the double Laplace transform to$t,t_{2}$ we will get: $$L_{t_{2}}(L_{t}(h(...
Volpina's user avatar
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1 answer
91 views

Transfer function $h(t)$ of a positive feedback system

I want to find the transfer function h(t) of the below positive feedback system. I came out till this. How can i get the inverse laplace of this function? say β = 1 and γ = 1
O-Negative's user avatar
3 votes
0 answers
42 views

Inverting transformation $\displaystyle m(t)=\sum_{i=1}^d x(i)^t$

Suppose there's a vector of $d$ of positive numbers $x(1),\ldots,x(d)$ which I need to obtain from a vector of $d$ derived quantities $m(t_1),\ldots,m(t_d)$ where $\{t_i\}$ is some conveniently chosen ...
Yaroslav Bulatov's user avatar
3 votes
0 answers
84 views

Discrete version of this transform?

I have the following transform for $t>0, a_i>0$ $$f(t)=\sum_{i=0}^d a_i \exp(-t a_i)$$ And I need to invert it for a set of target values $b$: Find $(t_0,t_1,\ldots,t_d)$ such that $f(t_0),f(t_1)...
Yaroslav Bulatov's user avatar
1 vote
2 answers
692 views

How we determine type of filter with pole(s), zero(s)? [duplicate]

Let's say we have this Laplace transform: $$H_{1}(s)=\frac{1}{(s+1)(s+3)}\;, \; \Re{e} (s)>-1 $$ So, we know that there is a poles at $s=-1$ and $s=-3$. With these informations, we found that to be ...
emrexx's user avatar
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1 vote
1 answer
103 views

Transfer function of LTI causal system

I have $$y(n)-3y(n-1)+2y(n-2)=4x(n)-2x(n-1)$$ that is the equation for a causal, discrete time LTI system. Using the Laplace Transform I rewrote it as: $$Y(s)-3e^{-s}Y(s)+2e^{-2s}Y(s)=4X(s)-2e^{-s}X(s)...
Anna Smith's user avatar
0 votes
2 answers
497 views

Finding transfer functions from a system of multiple inputs

If I have a system: $$sX(s) = AX(s)+BY(s)+CZ(s)$$ How would I find the transfer functions $\frac{X(s)}{Y(s)}$ and $\frac{X(s)}{Z(s)}$? Do I simply disregard one of the inputs? I am quite confused and ...
user66077's user avatar
1 vote
1 answer
29 views

How does the state estimate selection work?

I have been solving following problem. I have two open loop state estimators used for estimation of the unmeasurable states of a given linear dynamic system. The first estimator provides estimate $\...
Steve's user avatar
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1 vote
2 answers
219 views

First Order State Space Question

I am trying to understand the state space equation for a simple first-order LTI system. Suppose I have a system with impulse response $$h(t) = \frac{1}{\tau}e^{\frac{-t}{\tau}} \ \theta(t)$$ In this ...
solo's user avatar
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1 answer
65 views

Does the definition of stable system contradict itself?

A system is said to be stable when any of its poles are <0. However I don't get why that is the case. Negative poles mean negative angular frequency, and negative angular frequency is equal to ...
Miss Mulan's user avatar
1 vote
2 answers
104 views

What is the intuitive interpretation of the transfer function of this system?

If I have the system that could be observed in the next Image: I want to know the transfer function, where the external force $f$ is the entry and $x_1$ is the output. The direction and positive ...
Santiago Mercante's user avatar
2 votes
2 answers
795 views

Transfer function and Laplace domain

If we give a input $x(t)=u(t)$ to a system $\mathcal{S}$ we get an output $y(t) = e^{-t} u(t)$. After we Laplace-transform both the input and the output we get the transfer function $$H(s) = 1-\frac{1}...
Miss Mulan's user avatar
3 votes
1 answer
58 views

Name of property of Laplace transform

\begin{align} L[e^{-at}u(t)] &= \frac{1}{s+a}\\ L[\cos(\omega_{o}t)u(t)] &= \frac{s}{s^{2}+\omega^{2}_{o}}\\ L[e^{-at}\cos(\omega_{o}t)u(t)] &= \frac{s+a}{(s+a)^{2}+\omega_{o}^2} \end{...
Miss Mulan's user avatar
0 votes
0 answers
31 views

Amplitude ratio is larger than 0.5 on a RC-filter if RC = 1.7684e-03

I have two signals ...
euraad's user avatar
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2 votes
1 answer
483 views

Sampling with impulse train

There are many times when the textbooks used by all university students like me make an introduction to the notion of sampling of a continuous-time signal with an impulse train as shown below. Why do ...
Anastassis Kapetanakis's user avatar
1 vote
1 answer
189 views

Prove that the filter is stable, causal and minimum phase

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. This system, as ...
Mark's user avatar
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4 votes
2 answers
130 views

Study the stability of $H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. The degree of ...
Mark's user avatar
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2 votes
1 answer
312 views

What is the Laplace Transform of the output power spectrum if the input signal is a white noise?

Let us consider a random wide-sense stationary process $n(t)$, which passes through a filter $h(t, \tau)$. Its autocorrelation function is $$R_{n^\prime}(t)=\int_{-\infty}^{\infty} \int_{-\infty}^{\...
Mark's user avatar
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0 votes
1 answer
73 views

Reference for Wiener-Kolmogorov whitening procedure

In an old paper, accessible only for a fee, I found: (where the LHS of Eq (5) lack the symbol of derivative). What is the Wiener-Kolmogorov whitening procedure? I would like to study this procedure, ...
Mark's user avatar
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2 votes
1 answer
87 views

How does the phase/gain margin method work?

We have the closed loop transfer function: $$T(s)=\frac{L(s)}{1+L(s)}$$ So as far as I understand we check along the $j\omega$-axis on the Bode plot whether $L(s)=-1$, cause that's when $T(s)$ has ...
Kakukk777's user avatar
0 votes
1 answer
43 views

Time invariance in transfer functions

I read this in a book: here ${\cal L}[x(t-a)u(t-a)]$ is the laplace transform of a time shifted function $x(t)$ shifted by $a$ seconds and we know that transfer functions have the formula $H(s)=Y(s)/...
Sam1470's user avatar
2 votes
1 answer
711 views

Finding and displaying Laplace or Z transform ROC(region of convergence) using MATLAB

Is there any way, we can use MATLAB for finding and displaying Laplace or Z transform Region of convergence?
DSP_CS's user avatar
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0 votes
1 answer
101 views

Confusion regarding Laplace transform calculation in MATLAB

I am trying to learn about Laplace transform and especially about ROC and i found out on this weblink. I have also attached a snapshot of this link and highlighted where it is being said that although ...
DSP_CS's user avatar
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2 votes
2 answers
317 views

making a laplace s-domain plot from numerical data to decompose signal into decaying sinusoids

I would like to make a 3D laplace s-domain plot from experimental data I have. The examples I have seen for this are when the function is already known and an analytical solution can be obtained (...
Aaron's user avatar
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1 vote
1 answer
250 views

Laplace transform of derivative

Here is a short proof that Laplace Transform of $x'(t)$ is Laplace transform of $x(t)$ multiplied by s: On the other hand, the proof that I know uses integration by parts: One condition for the ...
mcr0yal's user avatar
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0 votes
1 answer
563 views

Bandwidth of a given function

Suppose the signal given is $x(t)=(cos(5t)+e^{-2t})u(t)$ and the goal is to find the bandwidth of this signal. We know the bandwidth, $B$, is just $f_{max}-f_{min}$. Our first step is taking the ...
Alexander Michalak's user avatar
4 votes
2 answers
917 views

Product of Doublet and Arbitrary Function

We know that the product of the delta function and another function samples the latter function. That is, $$ \delta(t-\tau)f(t)=\delta(t-\tau)f(\tau) $$ Does the doublet function retain this same ...
LetterSized's user avatar

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