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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6 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 ...
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0answers
26 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 ...
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1answer
30 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
27 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 ...
1
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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}} ...
2
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0answers
34 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 ...
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2answers
84 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 ...
4
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1answer
54 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
45 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 ...
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3answers
30 views

Lineart 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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20 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!
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2answers
59 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. ...
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1answer
27 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 ...
2
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1answer
68 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
29 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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2answers
37 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
87 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
101 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 ...
1
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1answer
57 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
33 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 ...
1
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0answers
20 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 ...
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2answers
80 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 ...
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0answers
24 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
60 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] = ...
2
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0answers
47 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 ...
0
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1answer
68 views

How do I show if this system is time-varying? [closed]

$\displaystyle y(t) = x(t), t \ge 0$ and $-x(t), t \lt 0$ I can anticipate this system is time-varying. However, I cannot be sure it and prove it. please help me.
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1answer
25 views

Is the system $L\{f[m,n]\}= c[m,n] f[m,n]$ shift invariant?

$c[m,n]$ is the spatially varying gain. My prof says that its not shift invariant. However if we put $m=m-k$ and $n=n-l$ we get $c[m-k,n-l] f[m-k,n-l]$ which is how a shift invariant system should ...
0
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2answers
34 views

Discrepancy when calculating LTI system output using inverse z-Transform

I'm given a difference equation, $y[n]-0.4y[n-1]=x[n]$, and asked to find the natural response $y_n[n]$, forced response $y_f[n]$ and complete response $y[n]$ if $x[n]=4 (0.25)^nu[n]$ and $y[0]=0$. ...
0
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1answer
111 views

BIBO stability and input at system's pole

My understanding of BIBO stability is that if a bounded input is applied to a discrete-time, linear, time-invariant BIBO system, the output will also be bounded. A sufficient condition for this is ...
0
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2answers
96 views

Output of a discrete-time LTI system different form than input?

This question is related to this one. I'm going through old exams for a 2nd year systems and transforms course, and came across this question. I'm posting this question just in case my other question ...
1
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3answers
96 views

Output of discrete-time LTI system guaranteed to be same form as input?

I know that in the continuous-time context, if I supply a complex exponential input to a Linear Time Invariant system, the output will be of the same form as the input - for example, if the input is ...
0
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1answer
43 views

Output of system defined by differential equation

I don't fully understand how the output of a system can be derived from the system's differential equation and a given input. For example: $$y(0-) = 1 $$ $$y'(0-) = -2$$ $$ u(t) : \text{Heaviside ...
2
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3answers
188 views

Does scaling property imply superposition?

For a system to be linear,it follow the principles of scaling and superposition.Does scaling imply superposition?If so why are two different conditions given for linearity?If not can u specify an ...
1
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1answer
63 views

System response: LTI system for $x[n] = \sin(\frac{\pi n}{4})$

Consider the LTI system with frequency response $$H(e^{j\omega}) = \frac{1-e^{-j2\omega}}{1+\frac{1}{2}e^{-j4 \omega}}, -\pi < \omega < \pi$$ Determine the output $y[n]$ for all $n$ if the input ...
0
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3answers
86 views

Uncorrelated but overlapping spectrum.

This answer may be straight forward but I cannot figure out. One can understand the difference between cross-correlation and convolution from the link below: What is the difference between ...
0
votes
1answer
54 views

LTI system impulse response output [duplicate]

If I have a LTI system which has impulse response $h(n) = \left(\frac{1}{2}\right)^nu(n)$ and the entry is $x[n]=u[n]-u[n-1]$ where $u[n]$ is the unit step function. In order to find the output I ...
1
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0answers
13 views

System indentification different inputs

I have peformed different form for input/output relation to determine a system, but seem to be missing some theory which input will be the most will excite enough modes such that the models which i ...
0
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0answers
46 views

Perfect system identification or am i doing something wrong?

I am using MATLAB to identify a system. The problem with my method is that my result is perfect. I get a nearly 100% fit, which make me wonder if what I am doing is correct. I feed a sine sweep with ...
1
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1answer
48 views

Beginner level : Help with terminologies : smooting length, length of channel, channel equalization delay, blind system identification, equalization

Say the channel model is an univariate FIR filter with true coefficients $h=[1,a_1, a_2 ]$. I am learning algorithms for system identification and channel equalization. For this, I am implementing ...
0
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2answers
98 views

LTI system, Fourier transform, unit step function, sine wave

I just finished learning about Fourier Transforms and don't understand this signal: $$x(t) = \cos(\omega t)u(t) $$ This is a cosine wave but only where $\omega$ is positive. My question is what can ...
0
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0answers
30 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
106 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?
0
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0answers
41 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.
0
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1answer
58 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, ...
1
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0answers
72 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 ...
1
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1answer
136 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 ...
1
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0answers
30 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 ...
1
vote
2answers
188 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
152 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: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...