A linear system operates on inputs with only linear operators so the response to a complex input can be analysed as the sum of the response to a set of simpler inputs. This mathematical property makes the analysis of linear systems much simpler than non-linear systems where this summation or ...

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28 views

How can I separate three noise sources?

This is the system I am trying to characterize I have three uncorrelated noise sources. I am trying to characterize all three noise sources, and more important find out what the original noise ...
1
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1answer
57 views

Output of lowpass filter with damped sine wave input

The random process $$Y(t)=\cos(\omega_0t)\cos(\omega_0t+\pi N(t))$$where $N(t)$ is a Poisson process of parameter $\lambda$ enters a lowpass filter with transfer function $$H(j\omega) = \left\{ \...
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1answer
29 views

LTI system input upsampling

Let's assume that a linear and time-invariant system is sampled at 2 different frequencies $F_{s}$ and $2F_{s}$ (e.g. 5Hz and 10 Hz). It gives $$Y_{F_{s}}(z) = H_{F_{s}}(z)X_{F_{s}}(z)$$ $$Y_{2F_{s}}(...
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2answers
60 views

How to modify an LTI differential equation to be acausal or anti-causal?

I'm trying to wrap my head around causality in LTI-systems. Considering continuous time only, I'm happy with the fact that the system is causal iff the impulse response function $h(t)=0$ for $t<0$. ...
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1answer
56 views

Why can adding delay improve the phase fit in fitting complex transfer functions?

When you fit an IIR filter to a complex transfer function you can use a delay to get a stable filter and improve the fitting results in your phase response. Can anyone explain me the reason for this ...
1
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1answer
44 views

$\mathcal Z$-transform ROC

Let's say I have a $\mathcal Z$-transform that represents some transfer function and its has some ROC. My question is how do I know if this system is causal? I know that if the ROC contains the ...
0
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1answer
28 views

Conditions for expressing a system as difference equation

I have read when studying this subject that a system is LTI and causal if and only if it can be expressed as a difference equation (if it is in continuos time, as a differential one). I don't know if ...
0
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1answer
32 views

LTI system response to periodic input

I'm trying to find the zero-state response (ZSR) of an LTI system to a one sided periodic input, like a square wave that is equals to zero for $t < 0$. I know that I can use the Fourier series of ...
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1answer
27 views

How to validate an estimated model in case of output-only data (in frequency domain)?

Before moving to the actual question, I would like to emphasize on the following points (maybe they are obvious to some of you, but I still would like to list them, since they make the difference): ...
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1answer
34 views

Proving conditions for controllability

Let's say I have the following LTI system: $$\dot{x}(t) = \mathbf{A} x(t) + \mathbf{B} u(t)$$ I need to somehow show the following is true or false (proof): This system is controllable if and only ...
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1answer
34 views

Are these Linear and Time Invariant Systems?

We were given the above systems and we were asked to tell whether they are linear (or not) and time invariant(or not). $y(m,n)=x(m,n)+c,\quad c>0$ $ y(m,n)=x(m,n)+x(m,-n)$ $y(m,n)=x(m,n+m)$ $y(m,...
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1answer
34 views

Showing a system is always controllable?

I need to show that the following system is always controllable: \begin{align}A &= \begin{bmatrix} -\alpha_1I_{k\times k}& -\alpha_2I_{k\times k}& \cdots &-\alpha_{n-1}I_{k\times k}&...
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2answers
56 views

Very basic questions about linear systems

Note: This question may seem extremely elementary, but I am not a beginner to signal processing, linear system theory, control theory, etc. I believe my confusion is over a subtle point, so, before ...
4
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1answer
68 views

LTI system without constant coefficient differential equation

I have encountered a system where the output $y(t)$ and input $x(t)$ are related in the laplace domain as: $$Y(s) = H(s)X(s) \tag1$$ which is typical. However, $H(s)$ is not a rational function of ...
4
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2answers
231 views

What is the difference between natural response and zero input response?

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
3
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2answers
67 views

How to show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$

I am trying to solve the following exercise: Show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$ (i.e. $x_n = w_1 x_{n-1} + w_2 x_{n-2}$). ...
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0answers
11 views

Kalman Filtering and space parametrization

I am familiar with Kalman filtering given a linear (time-invariant) state space model. However, the state space parametrization is not unique. Given a controllable and observable state space model (A,...
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2answers
71 views

What does “how to identify impulse response of a system?” mean?

I don't know where to start from, I'm not familiar with math. I'm trying to understand this question "how to identify impulse response of a system?". As you can see as below figure, as I know, the ...
0
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1answer
43 views

Inverse $\mathcal Z$-transform of system with an 8th order pole

Can I find the inverse $\mathcal Z$-transform of this transfer function: $$H(z)=\frac{1}{1-\alpha z^{-8}}$$ in a way other than contour integration and finding the residues of the 8 poles? If so, how?
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1answer
86 views

System characterization given pole-zero mapping

The figure shows the poleā€“zero plots for three different causal linear time-invariant systems with real impulse responses. Indicate which of the following properties apply to each of the systems ...
1
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1answer
67 views

Lowpass filter impulse response in frequency domain

A Linear Time-Invariant system with impulse response $h_1[n]$ is an ideal lowpass filter with cutoff frequency $\omega_c =\pi/2$. The frequency response of the system is $H_1\left(e^{j\omega}\right)$. ...
1
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1answer
34 views

Why is the total signal response response of zero input + zero state, $y(t) = y_0(t) + h(t)\star x(t)$, not an LTI?

For the zero input + zero state response in continuous time linearly time-invariant systems, why is the $y(t)$ equation not "technically" considered an LTI? I read this in a journal and there was no ...
0
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1answer
37 views

Guess stability based on filter coefficients

is it possible to guess the stability of a filter with given coefficients a and b? I know that the right way would be to calculate the pole positions and check if they are in the unit circle but I ...
0
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2answers
38 views

Intuition behind impulse response terms in convolution

We're learning about convolution in my signals and systems class right now. I have been able to do all of the problems by simply working out the respective sum/integral, but I'm still having trouble ...
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0answers
10 views

LTI system: solving for the time at which a system state reaches a given value

Suppose I have the following Linear Time Invariant (LTI) system: \begin{equation} \dot{x}(t) = Ax(t) + Bu(t) \end{equation} where $x(t)=\begin{bmatrix}x_1(t) & x_2(t) &\ldots &x_N(t)\end{...
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0answers
36 views

How to add single wavelength discrimination to the Kutulakos & O'Toole paper on a generalized Light Transport Matrix system

I wish to add single wavelength discrimination to the excellent paper Transport-Aware Imaging, Proceedings of SPIE Vol 9376, 937606 @ 2015 SPIE ,authored by Professor Kiriakos Kutulakos and Ph.D ...
0
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1answer
63 views

Channel Estimation / Equalization - Estimate Channel Inverse Using White Noise Statistics Only

Given the system defined in the following figure: We have a system $ G \left( f \right) $ which is unknown yet can be defined by $ {N}_{p} $ poles and $ {N}_{z} $ zeros. The signal $ x \left( t \...
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1answer
35 views

Is this system LTI?

Assuming the system $h[n]$ is LTI (and has an associated $H(z)$ transform), is the whole system below LTI? I found the impulse response of the system and I got that it is $$h_{0}[n]=\alpha ^{-n}\...
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0answers
28 views

Eigenvalues of correlation matrix which have the form of an harmonic function [duplicate]

As a continuation to this question, I took the matrix $C_{2 \times 2}$ which is: $$C=\left[ \begin{array}{} a& ace^{-\frac{|\phi_1-\phi_2|}{2}}\\ ace^{-\frac{|\phi_1-\phi_2|}{2}} &...
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0answers
37 views

Turn a decision problem into a linear filter problem

Let $x[n]$ be a time-series, and two filters: $A[n] = a_0 x[n] + a_1 x[n-1] + ... a_q x[n-q]$ $B[n] = b_0 x[n] + b_1 x[n-1] + ... b_r x[n-r]$ I think the answer is No, but is there a way to have ...
1
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2answers
98 views

How to obtain impulse response from the differential equation of a system?

This year I'm having trouble with my Signals and Systems class. My major subject is Software Engineering and Electric and Electrical Engineering is my Minor. This question was my previous exam ...
3
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1answer
70 views

Compute step response from impulse response of continuous-time LTI system

The impulse response of the LTI system is $$h(t)=e^{-4t} u(t)$$ The expression for the step response is $$\frac14 \left(1-e^{-4t}\right)u(t)$$ My question is how $u(t)$ appears in the answer.
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0answers
12 views

Input signals need to be sampled differently

I have a single output variable $y$ and a number of inputs $x_1$, $x_2$, etc. These are time series. Each $x_i$ explains the changes in $y$ in specific circumstances, and the goal is to have a linear ...
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2answers
54 views

May a causal system depend on future values of its own output

For example, let's assume a system given as y[n]-9y[n+2]=x[n] I convert the difference equation to y[n]=(y[n-2]-x[n-2])/9 ...
0
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3answers
66 views

Linear time invariance RLC

Why is a combination of R, L, C linear time-invariant system? But not diode, or transistor? I looked over V-I equation for R, L, C, but still don't know how to prove it.
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0answers
27 views

Assist on finding the impulse response fom a simple LTI graph

Could you please advise on the impulse response from this LTI graph? I need to plot it and find if it is stable and causal... Thank you!
0
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2answers
67 views

Why call it discrete time signals as difference equations?

There are lots of representations of discrete time signals. You represent it in block diagram or as difference equations. We call it block diagrams as there are elementary structures in the diagrams. ...
0
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1answer
31 views

Phase response for conjugate zeros

If a second order system has 2 poles/zeros that are conjugate symmetric, how does this affect the phase response? I know that if there are 4 zeros/poles that are conjugate reciprocals, then it is a ...
3
votes
1answer
109 views

Can someone let me know linearity, time-invariance, causality, memory characteristic of the system?

The input/output system is $$ \frac{dy(t)}{dt}+2y(t)=2x^2(t) $$ I want to know this is linear? causal? time-invariant? memoryless? According to solution, the answer is 'Linear if zero initial ...
0
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1answer
37 views

Can I use Fourier transforms instead of Laplace transforms (analyzing RC circuit)?

I don't study electrical engineering or something related but I was assigned a problem on transfer functions, impulse responses, and in general, everything related to this post. (Specifically, I'm ...
0
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1answer
54 views

find impulse response from step response

if we have LTI system and we know unit step response of this system(we haven't original signal) how we can calculate impulse response?
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1answer
127 views

How to estimate filters using conjugate gradient?

An image $I$ is computed by performing convolution and summation: $$ \sum_{k=0}^{K-1} z_k * f_k = I $$ Given only the feature maps $z_k$ and the resulting image $I$, how do I compute the filters $...
2
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1answer
173 views

How does one calculate a pole-zero plot?

To my understanding, pole-zero plots are used to analyze or visualize transfer functions. Suppose there is some very simple system, for example a simple low-pass filter (so it is linear and time-...
1
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1answer
184 views

Calculating frequency and damping ratio from transfer function given eigenvalues

I have the following standard transfer function for a damped linear oscillator: $$G(s) = \dfrac{\omega_0^2}{s^2 + 2\zeta\omega_0s + \omega_0^2}$$ Now I have two eigen values at locations $-100 \pm ...
0
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0answers
35 views

Comparing AR coefficients derived from different sampling rates

I'm interested in comparing the coefficients of AR processes computed from different dynamic texture videos. That is, $A_1$ and $A_2$ are the $d \times d$ coefficients for dynamic texture videos 1 and ...
0
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1answer
40 views

System Identification with periodic signal confusion

I want to find the ETFE (Empirical Transfer Function Estimate) of the system $G(e^{j\omega})$: Where $H(e^{j\omega})$ is some filter that zero-mean white Gaussian noise $e(k)$ passes through. Let's ...
1
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2answers
82 views

Why is it necessary to have two state variables

I am learning about control theory. Let's consider this system. $$ m a(t) + b v(t) + k x(t) = f(t) $$ $a$ is acceleration $v$ is velocity $x$ is displacement $f$ is external force In my ...
0
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0answers
28 views

FIR filter approximation using a continuous time dynamical system

How can you approximate a Finite Impulse Discrete filter (FIR) using a continuous time linear dynamical system with transfer function F(s)? I am seeing this problem using Matlab, where the resulting ...
0
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1answer
61 views

For filters with impulse responses on a specific $x[n]$, how do you calculate DFT of $y[n]$?

Basically I'm talking about N-point moving average/difference filters and not one where $\delta[n]=k$. For example given say a two-point moving average filter: $$h[n] = \dfrac{\delta[n]+\delta[n-1]}{...
2
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0answers
66 views

How to evaluate performance of an ARMA, MA or AR model?

How to evaluate performance of a model after estimating ARMA/MA/AR parameters for any process x(n)? How to regenerate back a process after estimating average parameters? what kind of performance ...