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Questions tagged [linear-systems]

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 superposition does not hold. Linear systems are generally further classified as time invariant, meaning that there characteristics do not change over time.

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83 views

Conversion from stationarity to non-stationarity

Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one?
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1answer
12 views

Causal LTI system having exponential input

I know that for an LTI system having complex exponential input, i.e, $x(t)=\exp(j w_o t)$ & $h(t) \to $ LTI System ; then, its output { $y(t) \} =M \exp(j w_o t + \phi)$ , where $M= |H(j w)|_{|w= ...
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1answer
46 views

How do you determine the properties of a differential equation?

If I was given a differential equation of the form $$y'(t) + a(t)y(t) = x(t)$$ how would I be able to decide its linearity, time-invariance, and causality?
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1answer
41 views

ROC of inverse system function

If the region of convergence (ROC) for system function $H(z)$ is $R_h$, what is the ROC of the inverse function $G(z)=\frac{1}{H(z)}$? $$$$
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1answer
28 views

expected value of two LTI output signals multiplied (cross correlation)

I have an input signal x (assumed to be iid Gaussian with $\mu=0$, $\sigma^2$) which is fed into two linear systems: $y_1 = h_1 * x$ $y_2 = h_2 * x$ Now I would like to calculate $\mathbb{E}[y_1 y_2]...
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1answer
70 views

Figuring magnitude and phase response

I've got a linear time-invariant system $$y[n]=\frac{8}{9}y[n-1]+x[n]$$ which I transformed into a transfer function $$Y(z)=\frac{8}{9}Y(z)*z^{-1}+X(z) =>\frac{Y(z)}{X(z)}=\frac{1}{1-\frac{8}{9}*z^{...
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1answer
228 views

Issues in generating AR model with a constraint

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

How to conclude LTI, causality and BIBO stability of a system represented by a differential equation?

I have started to learn about systems represented by differential equations in Oppenheim's Signals & Systems, and I got really confused about it. I am trying to understand how I can show that a ...
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1answer
67 views

The Spectrum of the Impulse Response of Linear Time Invariant (LTI) System

Consider an LTI system with impulse response $$h[n] = \frac{1}{5^n} u[n].$$ (a) Determine and sketch the magnitude and phase response $|H(\omega)|$ and $\arg(H(\omega))$ respectively. (b) ...
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1answer
85 views

Modeling an infinite delay system

If black holes swallow everything and assumes that the black holes do not get out the things from them, then can we consider a black hole as an infinite delay system? It takes the input and it is a ...
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1answer
472 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} = \...
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60 views

How to implement the RLS for matrices

I need to implement the RLS algorithm but it's for matrices instead for vectors, I have made the below code, but still something wrong is not working well, EDIT: The code should be done as below, ...
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0answers
68 views

How to derivate in the frequency domain

I have two Time Domain functions, $f_1(t)$ and $f_2(t)$. I have both Fourier Transforms, $F_1(\omega)$ and $F_2(\omega)$. Functions $f_1$ and $f_2$ are not independent and, in fact, $f_1$ is also a ...
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0answers
92 views

Check if I has right: Is this the Extended Kalman Filter

I have learn the Kalman-Buncy filter for the LQG controllers. I know that this is a signal processing forum and not robotics not math forum. But Extended Kalman Filters are daily discussed here. ...
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0answers
142 views

How does the ROC (Region of Convergence) related to a real world application?

In class, we are often given exercises to find the impulse response, output, and Z-transform of a system. In addition, we are often asked to define the Region of Convergence (ROC) depending on where ...
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0answers
214 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 ...
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0answers
31 views

Moving average and linearization of two piecewise linear systems

I have 2 oversampling ADC's running parallelly, each to process data in a specific range of the input as shown below: Each ADC can process only half cycle range of a sine wave. Each ADC adds its own ...
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0answers
20 views

How to obtain the steady state response of the sampled periodic signal data?

Below the green plot Vin is 5Hz sine voltage signal from a function generator output sampled at 12kHz sampling rate: The blue plot Vout is the processed/filtered data by using the following code in ...
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0answers
99 views

Linear Predictive Coding example in MATLAB

I have some data that is highly correlated and I wanted to see if I could try and encode it using linear predictive coding (LPC). Here is how I've been understanding the process: Encoding Generate ...
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0answers
38 views

Understanding linear predictive coding in MATLAB

I want to test my understanding of linear prediction by running it on some test data in MATLAB. The way I understand it is if I have some data that is correlated, I can encode the signal with linear ...
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0answers
18 views

Finding the component vectors for a grid of points

I have a 2d 'grid' of xy points (2000 of them). I want to find the average vector between points I have drawn the vectors on the graph, how do I find these vectors mathematically? I want to find the ...
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0answers
76 views

Why prediction by AR model causes time lag

Why does prediction by AR model cause a time lag? Please tell me why theoretically.
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0answers
59 views

identifying overshoots in given state space system with step inputs

Suppose I have the following state space system: $$ \dot{x}(t) = Ax(t) + Bu, \quad y(t) = Lx(t), \quad x(0) = x_0 $$ where $A$, $B$ and $L$ are real matrices, $u$ is a constant real vector (so that ...
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0answers
51 views

Variance and Co-variance of a Linear Forecast

Consider a linear forecasting problem where all shocks $\{\epsilon_i\}_1^n$ are independently distributed with $\epsilon_i\sim N(0,\sigma_i^2)$ for all $i$. Suppose you want to forecast $\theta = \...
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0answers
27 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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0answers
46 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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0answers
126 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 can'...
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0answers
90 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 \boxed{\...
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0answers
49 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 ...
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0answers
489 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, ...
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0answers
23 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 u2*I*P2=u2*...
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33 views

Linear difference equation and method of Least Squares

I'm reading the book "Fault-Diagnosis Systems" by Isermann in the par. 9.2.1a. The author explains how to estimate the parameter of a linear difference equation using Least Squares. We start with a ...
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22 views

Co-prediction of signals

Is there any plausible method to estimate or predict one signal, on the basis of known value of another signal, provided the two signals bear a strong correlation? For instance, the audio amplitude ...
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0answers
21 views

Relationship between signal amplitude and input output correlation

I have a linear system with input $ x(t) $ and output $ y(t)$ given by $$ y(t) = \int_0^\infty K(t')x(t-t')dt', $$ where $K(t)$ is a known kernel, with some parameters. The functional form of $K(t)$ ...
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56 views

Relationship of the cross correlation and the amplitude of the signal

I would like to characterise the maximum amplitude $|x(t)|$ (or similar quantity $|x(t)|$ or $|x(t)|^2$) of the following linear system $$ x(t) = \int_0^\infty K(t')S(t-t')dt',$$ where $ S(t) $ is ...
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26 views

Complete Response Linear System

I couldn't find out the answer for item d.
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0answers
37 views

Recursive systematic convolutional code with TCM

My question is: What are the outputs from the TCM encoder ?
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0answers
66 views

Frequency Response Question on LSI System

Someone please explain me the question its seems very complicated to me. I just want know what the question asking and how to solve it i dont want fully solved solution. Thank you!!
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0answers
22 views

should block diagrams in Direct Form 1/2 contain empty branches to fit structure?

When creating a block diagram in a well-recognized structure (Direct Forms 1&2 in particular), does one remove branches where the coefficient is 0? This picture includes a coefficient of $b_1=0....
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157 views

How to determine if a system is LTI from the frequency response function?

I was told that the FRF should be a linear function of $\omega$ for the system to be linear. So for a harmonic oscillator, with an FRF given by $$H(i\omega) = \frac{1}{\sqrt{\left(\omega_0^2 - \omega^...
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0answers
72 views

DSP Homework Help - Proofs and Causality

I'm completing my last semester of university and for my last EE minor course, I had only one option available, an Audio and Speech processing class. Safe to say, it's difficult for me and would like ...
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125 views

Fourier transform and duality

Consider continuous even signals $x$ and $h$ with spectra $X$ and $H$. Now consider LTI system $L_1$ characterised by IMPULSE response $h$. When $x$ is the input in $L_1$, the output is $y_1$ with ...
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65 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 ...
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0answers
26 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 ...
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0answers
69 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 ...
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265 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 things:...
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42 views

Basic question about Block Diagrams and Scale factor

I am doing a project about controlling a thermoelectric module, and for doing so I must reverse the current direction. This is achieved changing the voltage polarity. So the output of the controller (...