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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20 views

Is this expression true? [on hold]

Is this expression true? In Non fractional and Non radical systems,if condition of homogeneous is satisfied,the system is linear.
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34 views

Block diagram system response

I have this system of equations: $\ h_1(t)=\delta(t-1)$ $\ h_2(t)=\exp(-2t)u(t)$ $\ h_3(t)=\delta(t-1)$ $\ h_4(t)=\exp(-3(t+2))u(t+2)$ And this block-diagram: I need to find the total ...
2
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1answer
117 views

Does instability make an otherwise LTI system nonlinear (or time-variant)?

okay, i am spinning this question off from the question from johnny. @MattL. and i have had directly opposite conclusions to johnny's question. i want to decouple the question from issues of ...
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1answer
32 views

How to periodically estimate states of a LTI if the output is measured irregularly?

How can I periodically estimate the states of a discrete linear time-invariant system in the form $$\dot{\vec{x}}=\textbf{A}\vec{x}+\textbf{B}\vec{u}$$ $$\vec{y}=\textbf{C}\vec{x}+\textbf{D}\vec{u} ...
2
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3answers
229 views

Is this system linear?

I have this system: $$ y[n] = -\frac{1}{2} x[n+2] - y[n+1] $$ I have no idea how to prove if the system is linear or not, because, it depends on future outputs... Thanks for the help
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2answers
92 views

Checking linearity/time-invariance etc. for recursive system

I'm familiar with the general methodology for checking if a system is linear: Define output $y_1[n]$ for input $x_1[n]$, define output $y_2[n]$ for input $x_2[n]$ Define $x_3[n] = ax_1[n] + bx_2[n]$ ...
0
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1answer
49 views

Natural, Forced and Total System Response - Time domain Analysis of DT

I am a self-learner of DSP by reading related books. While reading Time domain Analysis of DT (Discrete Time) system, I suddenly got introduced to difference equation representing a system. It then ...
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2answers
52 views

Time variant and Time Invariant Systems

I was trying to solve the below system is a Time variant or Time Invariant System: $y(n)=nx^{2}(n)$ Now for a system to be time invariant the system property should be : ...
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1answer
35 views

What are some example of applications for LTI systems

I'm giving a lecture on LTI systems. I encountered some questions: for a discrete LTI system H with impulse response h, is the system applied on signal x(t) equals x*h - normal discrete convolution ...
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0answers
22 views

Low dimensional system identification algorithms

I'm a physics Phd student and just have a self-taught knowledge about lti-systems. After a while I found out that several techniques such as heat capacity or thermal-conductance measurements can be ...
0
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1answer
34 views

Introduction to Clustering and Classification of Linear Sequence

I'm a programmer/engineer that is getting into developing prototype wearable technology. I would like to be in a position to interpret raw accelerometer data and categorised the data into activities ...
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1answer
43 views

Impulse response of the inverse system to the backward difference

I'm currently stuck on a problem. I have a DT LTI system $\mathcal{T}$ that depicts the first backward difference: $$y[n] = \mathcal{T} \{ {x[n] \} } = x[n] - x[n-1]$$ Its impulse response is ...
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1answer
42 views

Compute output of a LTI system

Is it possible to compute the output from one linear time invariant system which unit impulse sequence is: $$h(n) = \left(\frac{1}{3}\right)^nu(n)$$ and the entry in the system is: ...
0
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1answer
63 views

How to find the output of a system with the unit-step response and the input?

Convolution is used to find the output when the input and the impulse response is known. I am curious if there is a similar operator, like convolution, or a method that can determine the output of a ...
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1answer
101 views

How to determine if a system is LTI?

If the difference equation that defines the DT system is, $$z[n] = (1-x[n]) + (1-y[n]) $$ How can we determine in the system is LTI or not when: $x[n]$ is the input $y[n]$ is the input both are ...
0
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1answer
79 views

First-order low pass filter with bounded derivative

Given a function $x(t)$ and a first order low-pass filter $\frac{dy}{dt} = \frac{1}{\alpha} (x(t) - y(t))$, is there a way to choose $\alpha$ analytically such that the derivative of $y(t)$ is ...
1
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2answers
108 views

Causality of Linear Phase Filter

If a digital LTI filter has phase response on the form $arg[H(e^{jw})] = -\alpha\omega$, what could one say about it's causality (and consequently, the causality of it's impulse response)? Also is ...
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1answer
49 views

Conceptual question from signal processing: impulse response and linear regression

In continuation to the previous question Conceptual questions from signal processing I have a doubt which is : Consider an Autoregressive model (AR(2)) : $y(t) = ay(t-1) + by(t-2)$ and a FIR (Moving ...
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1answer
33 views

Linear classification and overlapping problem reduction

I am study linear classification(Y=aX+b) But it is still weakness that is overlapping problem. Could you suggest to me how to reduce overlapping problem in linear classification or how to find these ...
2
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0answers
49 views

Performance of adaptive signal processiong algorithm in noise not working

I am taking a course on signal processing and have been looking at various algorithms performance in presence of additive noise of different SNR. I was implementing Least Mean Square (LMS) algorithm ...
0
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1answer
76 views

Issues in generating AR model with a constraint

I am new to the topic of system identification and looking for a large model of Autoregressive (AR). Can anybody point out a large stable AR model which has more than 2 coefficients AND there should ...
0
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1answer
46 views

Is the following system LTI (finite speed of signal propagation)?

I wonder if the following acoustic system is i) considered to be linear time-invariant, and ii) if it is fully described by it's frequency response? A speaker produces waves at the input location of ...
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1answer
74 views

Relationship between Discrete Deconvolution and Toeplitz Matrices

I have 2 vectors, $a$ & $c$, both of length M. I know they are related by $a*b=c$. My goal is to recover $b$. Obviously $b=$deconv$(c,a)$. I am only interested in the first M elements of the ...
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0answers
51 views

Coefficient Cancelation on Particular Solution

I am stuck on a problem about finding the complete solution of a Discrete Linear System by using the parametrization $y_{c}(n) = y_{h}(n) + y_{p}(n)$ where $y_{h}(n)$ and $y_{p}(n)$ are, respectively, ...
3
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2answers
72 views

Impulse Response with non-delayed feedback

I've been trying to solve a Discrete LTI System problem where the overall impulse response of the following System, whose input and output sequences are, respectively, $x(n)$ and $y(n)$, has to be ...
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1answer
79 views

How to calculate the zero state response?

In the following question and answer I kind of get it how it is calculated at surface but I don't get it fully. Can someone please explain the answer in depth?
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2answers
117 views

Criteria to distinguish FIR and IIR filters from difference equation?

What criteria should be used to safely decide if it is an IIR filter or FIR filter from a difference equation? FIR filter are always stable, meaning all poles are inside the unit circle AND have ...
3
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2answers
99 views

Can I construct a linear system so that it results in a moving average?

I've just learned about linear systems and impulse response functions. I know that in a linear system consisting of $h_1[k]$ and $h_2[k]$, the impulse response of the system is $h_1[k] \ast h_2[k]$. ...
0
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1answer
194 views

The impulse response, $h(t)$, of a system

I have this differential equation $$ y''(t) + y'(t) + y(t) = x(t) - 3x'(t) $$ I found the system response of the system: $$ H(f) = \frac{1 - 6\pi fj}{(2\pi fj)^2 +2\pi fj+1} ...
3
votes
2answers
69 views

Deconvolution with an underdetermined system of equations?

If I have a measured signal $\mathbf{y}$ which is the result of the true signal $\mathbf{x}$ convolved with another function (linear and not circular convolution), I always seem to get an ...
0
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0answers
160 views

Solving linear system and find impulse response

I have this linear system that is defined by the differential equation $$ y''(t) + 4y'(t) + 5y(t) = 2x(t) + 3x'(t) $$ with x(t) the input and y(t) the output. I'm asked to find two ...
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41 views

Using output error model to model colored noise (using a prefilter)

I have a "black box" SISO system. I use zero input to measure pure noise on the output. After preprocessing (peakshave and removing DC) I try to model the noise using AR (and also ARMA). When ...
0
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0answers
18 views

Affine Non Autonomous State Space System

Normally We all know the state space model of the the form $$\dot{x} = Fx(t)+Gu(t)$$ $$y = Hx(t)+Ju(t)$$ However I came across a state space model which has the following form $$\dot{x} = ...
0
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1answer
346 views

Convolution of a signal by itself properties

I'm studying for a test and I can't really explain this question very well. If we convolve a signal by itself, will it have the same properties (time-invariant, linear, stable, casual)? I know how ...
5
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1answer
171 views

Are complex exponetials the only eigenfunctions of LTI systems

Can I have an example of eigenfunctions of Linear Time Invariant(LTI) which is not a complex exponential? This document: Eigenfunctions of LTI Systems says such eigenfuctions do exist. But I am not ...
7
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3answers
131 views

Is there a way to obtain the impulse response of a discrete system by just knowing it's response to the discrete unit step function?

In continuous time it was possible; $$\Large u(t)\rightarrow \Large{\Box}\rightarrow y(t)$$ $$\Large{\delta(t)=\frac{du(t)}{dt}\rightarrow \Box\rightarrow \frac{dy(t)}{dt}=h(t)}$$ Does the same apply ...
1
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1answer
84 views

What filter is better with -1/3 2/3 -1/3 or with -1/4 1/2 -1/4 coefficients?

Professor asked me what filter is better -1/3 2/3 -1/3 or -1/4 1/2 -1/4, the answer was second. But what those coefficients means? It was during discussion of linear filter but i'm not sure was it ...
2
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1answer
237 views

Causal systems - Paradox? Confusion of definition?

For a system such that $y[n]=cos(x[n])$, I'd like to determine whether the system is causal or not. Definition 1: A system is causal if and only if the output $y[n]$ is a function of a linear ...
0
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1answer
118 views

Determining linearity, causality, memory, and time invariability from a picture of the signal

So, this is a picture of saccadic eye movement reflected by an EOG. How can I determine if the eye movement system is linear, causal, memoryless, and time invariant from this displayed waveform? ...
1
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3answers
322 views

Sum of Sine and Cosine with Random Phase as LTI System

I have the following system: Where $ {H}_{1} \left( f \right) = {H}_{2} \left( f \right) $ and $ \theta \sim U[0, 2\pi]$ independent of any other factor in the system. Given the input is identical, ...
2
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1answer
72 views

Choosing inverse Z-transform equation, given that $|a|<1$

Given that $|a|<1$, then which of those inverse-Z-transform equations are we to use? I am leaning towards the first because (as I understand it), $z$ is merely a complex number that is ...
3
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0answers
50 views

Ideas on matrix factorizations and/or transformations for $\ell_1$ minimization

I am starting with a typical $\ell_1$ basis pursuit problem: $$ \min_{\mathbf{x}} \Vert \mathbf{x} \Vert_1 \quad \mathrm{s.t.} \quad \Vert \mathbf{ERx} - \mathbf{y} \Vert_2 \leq \epsilon, $$ where ...
2
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2answers
113 views

Situations where complexity is too big to exceed linearity and gaussianity

I'm studing about Kalman Filter and Particle Filter in multiple target tracking in computer vision (tracking pedestrians). Reading sientific papers I'm colliding with a lot of sentences like: The ...
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0answers
19 views

Panorama global registration

I'm trying to do global registration algorithm for panorama like described here. But I don't understand how they deal with false pairs. Also if expand the system u1*I*P1=u1*I => P1=I ...
3
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2answers
141 views

Frequency response of system with feedback and feedforward co-efficients?

For seismological application, I am playing with an elliptical filter, and once I have both sets of feedback and feedforward co-efficients, how do I make it so that I can plot the frequency response ...
2
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2answers
5k views

What is the difference between Lumped and Distributed systems?

What are the salient differences between Lumped and Distributed systems? In what contexts are distributed systems the appropriate model and in what are lumped systems the appropriate model? Also, ...
3
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1answer
230 views

Impulse Response Question

For the differential equation $$\frac{d^2y(t)}{dt^2}+\frac{3dy(t)}{dt} + 2y = x(t),$$ I was able to find the frequency response as $$H(j\omega)= \frac{1}{-\omega^2+3j\omega+2}.$$ However, I am not ...
1
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1answer
104 views

How can frequency dispersion in a vibrating string be modelled using an LTI filter?

According to JOS on stiff-string synthesis, stiff strings (like on a piano) introduce inharmonicity (i.e. the harmonics of the tone are not all in tune) due to different frequency components of the ...
3
votes
1answer
137 views

How to perform model fitting for system identification

I am having a really hard time in understanding how to formulate a model say linear AR model to represent a communication channel or maybe any motion. I have the experimental data representing the ...
4
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1answer
342 views

Problem with the definition of Linearity

From the high school maths we know that y=mx+c is a linear equation. However, in DSP the linear system must satisfy Additivity properties which y=mx+c does not hold because of +c. So, is the ...