# 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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129 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, ...
35 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 ...
98 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 ...
119 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. ...
210 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 ...
334 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 ...
40 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 ...
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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### 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 ...
55 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 ...
172 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 ...
666 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 ...
95 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 ...
83 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?
35 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 ...
134 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?
91 views

### Why prediction by AR model causes time lag

Why does prediction by AR model cause a time lag? Please tell me why theoretically.
66 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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### 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 ...
70 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 ...
237 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 ...
280 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:...
162 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) ...
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} = \...