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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132 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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52 views

linear minimum mean squared error estimate under Gaussian prior

I am learning estimation theory through Steven M.Kay's book Fundamentals Of Statistical Signal Processing--Estimation Theory. In the ...
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82 views

Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$

Let $$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$ Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$? If not, what's the reason for ...
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1answer
57 views

What are the properties of continuous-time improper systems?

I am trying to better understand the properties of improper systems $H(s) = \frac{b(s)}{a(s)}$, for which the order of the numerator $b(s)$ is greater than the order of the denominator $a(s)$ (in the ...
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142 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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128 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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226 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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424 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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106 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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99 views

Time-Invariant (non)autonomous Systems

Regarding potential distinctions between autonomous, non-autonomous, time-invariant and time-varying systems, I have found out opinions supporting that: autonomous systems are time-invariant and non-...
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1answer
31 views

Determining if the system is linear and time invariant

The Fourier transforms of input $x[n]$ and output $y[n]$ of a discrete-time system are related by the following equation: $$Y(e^{j\omega}) + (e^{-j\omega})Y(e^{j\omega})= X(e^{j\omega}) - X^{'}(e^{j\...
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1answer
44 views

Finding the system output by convolution

pretty new to this concept, so do bear with me. A linear dynamic system is described by the following differential equation: Transfer function H(s) is calculated to be = I've already found the ...
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35 views

Trouble checking if a given difference equation corresponds to an LTI System

I'm having trouble on how to check if a given difference equation corresponds to an LTI system. For instance, Does the following difference equation correspond to a LTI DT system ? Explain. $$y[...
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49 views

Determining if a 2D system is LSI

After a long time away from school, I'm a bit rusty and struggling with this question: Determine if the following discrete system is LSI: $y(m,n) = mn*x(m+n) + mn*x(m-n)$ So here's what I've done ...
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33 views

Does phase margin exists only for linear systems?

If possible, how to determine the phase margin for nonlinear systems?
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109 views

Region of convergence of transfer function

I posted this question Mathematics SE and got no answer so I have posted it here. I learned in my signal processing class that an LTI system can be defined using a linear constant coefficient ...
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77 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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226 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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941 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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104 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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52 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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2answers
144 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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94 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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68 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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53 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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29 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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47 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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153 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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51 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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591 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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24 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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1answer
13 views

Implementing an L-System conversion from R2 to R1 for symmetric, square matrices

I have been reading for some time about L-Systems, and specifically the Hilbert Space filling curve. I am interested in writing a function to convert upper-triangular matrix coordinates into an ...
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29 views

Is a LTI system with dead-time equivalent with a LTI system with no dead-time but delayed input signal?

I wonder if the system parameters would remain the same after all. According to the definitions, the gain is the change of the output induced by the change of the input if we assume that the gain is ...
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1answer
54 views

Determine the haar wavelet function is linear or nonlinear

I'm looking for analytical justification of linearity or non linearity of the wavelet transform with the real Haar mother wavelet function. I have googling already. But I can't find and understand ...
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24 views

Characterizing a non-LTI system

How should we characterize a non-LTI system? For example we have: $y[n]=x[3n]+x[2n]+x[n]$ which is clearly not LTI. Also, the impulse response will be $h[n]=3\delta[n]$ and if we take the DTFT of this ...
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27 views

Discretizing my continuous system in Matlab

I was hoping someone could help me with conducting my discretization in MATLAB. I have a linear system with known data: sampling interval $T$, system matrix $\mathbf{A}$, input matrix $\mathbf{B}$, ...
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53 views

Phase response of an LTI-system

I've got an LTI-system such as follows: $$y'(t)+{2} y(t)={5} x(t-{3}), t>0, \\ \\ y(0)=0 \ \text{ ja } x(t)=0, \ t<0.$$ From this i've already figured out the transfer function: $$H(f)=\frac{5\...
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1answer
56 views

how do I derive the system equation for a simple delay with feedback?

I am a software engineer, and just learning digital signal processing formally, though I've hacked around before a fair amount. I'm implementing a delay audio VST and I'm trying to wrap my head ...
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1answer
37 views

Controllability's dependence on B matrix

Assuming the LTI system: $\dot{x}=Ax+Bu\\$ , where $x\in R^n$ I understand that the $B$ matrix is usually given, and it is up to us to derive the optimal $u$ given an initial state of the system ...
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24 views

Inversion problem for big dataset

Suppose my goal is to solve for $x$ in $Ax = b$ using CG method and $A$ is Toeplitz. The problem is that $b$ is extremely large in size and I can't just read in the whole vector $b$ and then solve for ...
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1answer
96 views

How does one describe the “frequency response” of a mixer?

Suppose one uses a vector network analyzer to measure the $S_{21}$ parameter of an RF mixer over a frequency range. Would it be appropriate to call this the “frequency response” of the mixer? I find ...
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1answer
73 views

What does this notation $g(x) = S\{\delta(t) \}(x)$ mean?

What does this notation mean $g(x) = S\{\delta(t) \}(x)$ mean, where $S$ is a "system", $\delta(t)$ is the impulse function and $g(x)$ the output function of the system? I am really not familiar with ...
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47 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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97 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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3answers
183 views

Causality as applied to capacitors

This question stems from a point of confusion that I still have about the causality, linearity, and time-invariance in LCCDEs. I wanted to use the capacitor as an example. Consider a capacitor with ...
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65 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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27 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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72 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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1answer
240 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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284 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:...