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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26 views

Estimation of Hit Time Using Kalman

I have the following model for Kalman Filter. The Dynamic Equation: $$ \begin{bmatrix} {r}_{k} \\ {v}_{k} \end{bmatrix} = \begin{bmatrix} 1 & -T \\ 0 & 1 \end{bmatrix} \begin{bmatrix} ...
1
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1answer
79 views

What is the physical interpretation of the dB scale on a bode plot and what is a negative dB?

I have no physical interpretation of the Bode plot. What does it mean for a bode plot to have negative dB over its entire duration on the log-scale frequency?
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0answers
24 views

How to compute h(t) for a causal LTI system

For example I have given this equation : y''(t) + 3y'(t)+y(t) = x(t) How can I compute h(t) for this? Thanks.
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1answer
30 views

Derivative Notation as a factor

In the figure below, from the book "Principles of Linear Systems and Signals - Lathi", the author uses the notation D to replace the Leibniz's notation $d/dt$, and after that he rewrites the equation, ...
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0answers
58 views

Basic “filtering” in digital communications

I am completely stuck on solving some problems for my digital communications class. Junior level undergrad class, so fairly basic. I have been searching around all day for related articles etc but ...
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0answers
17 views

Reference Request : How to compute CRLB to show the estimator is minimum variance

In system identification or parameter estimation, various input signals are used for exciting the process models. I am interested in parameter estimation of time series model using pseudo random ...
1
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1answer
38 views

The two types of stability and “Why exponential”

When I was learning about LTI systems, I noticed that LTI system is said to be BIBO stable if and only if its square sum of impulse response is finite. This expression is found on many textbook of ...
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0answers
22 views

How to make equivalent system using the Noble Identity?

I am trying to get equivalent of this system using the Noble Identities: $$x[n] \rightarrow \boxed{H(z^L)} \rightarrow \boxed{\uparrow L} \rightarrow y[n]$$ my answer is $$x[n] \rightarrow ...
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2answers
66 views

How to prove that frequency mixer is a nonlinear system?

I know that frequency mixer $y(t)=x(t)cos(\omega_ct)$ is a nonlinear system since its output has frequency components that are not present in the input. To prove its nonlinearity, it shuldd be shown ...
1
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1answer
49 views

kalman filter with time-varying noise?

in regular discrete-time (1 dimensional) kalman filter, it is assumed that we have white gaussian noise affecting the transitions and the observations: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...
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3answers
73 views

Alternative to BIBO stability of a system

In DSP textbooks a system is stable in the BIBO (Bounded-Input, Bounded Output) sense if and only if every bounded input sequence produces a bounded output sequence. After stating this definition ...
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1answer
62 views

Ideal BandPass Filter

Let suppose x(t)=$\sum\limits_{k=-∞}^∞ R(t-kT)$ $R(t) = \begin{cases}1 &[0,2T] \\ 0 & \text{otherwise} \end{cases}$ x(t) is the input to an ideal bandpass filter with $\text{BandWidth} = ...
6
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1answer
99 views

How to find the CRLB: Help in understanding the steps in paper

An univariate autoregressive process AR(p) process is expressed as $$y(n) = \sum_{j=1}^p a_jy(n-j) + u(n) $$ is excited by Gaussian sequence, $u$. Is there a resource / reference for a lucid ...
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1answer
132 views

System Properties; Linear, Causal, Time-Invariant, Stable?

I know the answers of the below question but I dont know why, except linear, could you explain the rest? Small tick: correct, small tick with dash incorrect answer.
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1answer
40 views

LTI system output

I compute the output of a LTI system, can someone tell me if my answer is right..? and help me with my others questions? The impulse response is: $h(n) = \left(\frac{1}{2}\right)^nu(n)$ , entry is ...
0
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0answers
29 views

Is the inverse of the inverse of a system the same with the original system?

We know that series combinations of LTI system are commutative, meaning that changing their order does not change the whole system. But it is not the case for all systems generally. Now, if we put ...
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2answers
48 views

Fit a line pattern on curve with unknown number of points

I've got a sample curve which ends theoretically with decreasing exponential. The curve end falls into noise. The sample points are given in log scale. What I want to do, is to find and fit the linear ...
1
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1answer
93 views

Do Causal Discrete-time systems have proper transfer functions?

In the case of continuous-time systems, if the system is causal, its Laplace transfer function is strictly proper (the degree of the numerator is less than the degree of the denominator). Is this ...
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2answers
93 views

Can I see from the PSD if a system is a LTI system?

I am studying the meaning of the power spectral density (PSD) and I am wondering whether I can see from the PSD of the input signal and output signal if a system is a LTI system?
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2answers
75 views

Is this HW question even valid? (linear systems)

The question is: Are the following systems linear time invariant? $y(t)=x(t)$, with $x(t)=u(t)$ (unit step function) $y[n]=x[n]$, with $x[n]=\delta[n]$ (Dirac delta function) The reason I am ...
1
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1answer
181 views

Is digital up and down sampling linear/causal/time-invariant?

So I am trying to determine whether the process of up sampling (zero padding) and downsampling are linear, causal and/or time-invariant. Based on some resources I found online, I am under the ...
0
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2answers
47 views

How do I take the real part of this bandpass filter system's output?

I'm stuck on a final step in this problem. Essentially, there are the two systems above, which we'll call System 1 (Fig. 4.26, with ideal lowpass $H(jw)$) and System 2 (with $H_1(jw)$). The ...
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0answers
34 views

Choosing an appropriate PRBS for system identification

The system im investigating can be approximated with a First Order plus deadtime model. I'm currently using step and doublet pulses(two steps with opposite sign) to excite the system. I'd like to use ...
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0answers
42 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 ...
4
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3answers
199 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 ...
0
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1answer
52 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
votes
3answers
262 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
296 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
votes
1answer
136 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 ...
0
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2answers
258 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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votes
1answer
74 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
25 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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3answers
63 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 ...
0
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1answer
88 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 ...
-2
votes
1answer
77 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
135 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 ...
1
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1answer
158 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
98 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
119 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 ...
0
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1answer
60 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 ...
0
votes
1answer
34 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
votes
0answers
72 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
105 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
50 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 ...
1
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1answer
143 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 ...
1
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0answers
86 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
votes
2answers
82 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 ...
1
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1answer
226 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?
1
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2answers
147 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
votes
2answers
104 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 $h_1[k] \ast h_2[k]$. ...