10 votes
Accepted

Difference between causality and memorylessness

A causal system does not need to know the future in order to compute its output. A memoryless system computes the output only from the current input. A memoryless system is always causal (as it doesn'...
Matt L.'s user avatar
  • 90k
7 votes
Accepted

Protect an IIR filter from being reverse-engineered

Short answer: You can't. If an attacker can insert a signal that covers the whole bandwidth (e.g. a white signal, or at least one that has no spectral zeros) into the system (and he can do that over ...
Marcus Müller's user avatar
7 votes
Accepted

Does the error in the impulse response accumulate when applying a step-input?

As written $e[n]$ does not pass through a high pass filter but is presented to the same input as $Bu[n]$. The block diagram and subsequent equation would appear as follows: We see noise growth as we ...
Dan Boschen's user avatar
5 votes
Accepted

Determine whether the system is linear?

In the following, I suggest that, before using the generic $T(\alpha_1 x_1+\alpha_2 x_2)$ versus $\alpha_1 T( x_1)+\alpha_2T( x_2)$, it can be more informative to try with simpler partial tests, or ...
Laurent Duval's user avatar
5 votes
Accepted

Check if the system is linear

I believe there's either a mistake in the presentation or the presentation is using a different definition of linear. For example, the system is linear in $x$ from a system perspective, but it's ...
Peter K.'s user avatar
  • 25.7k
5 votes

As of 2019, which discrete nonlinear, time-invariant systems with memory are considered "easy" to model and identify?

It is very strange phenomena that one object is completely dropped out of attention of researchers. It is Urysohn operator. First of all Urysohn is equivalent to multiple parallel Hammersteins and ...
Andrew Polar's user avatar
4 votes

Recursive system

No, it can be rewritten as $y[n] = x[n]/2$. Basically, the output is the input divided by 2...
Ben's user avatar
  • 3,777
4 votes

Difference between causality and memorylessness

A memoryless system's output is determined by the current input value only, hence, every memoryless system must also be causal (a system is causal if its output does not depend on the future input ...
Fat32's user avatar
  • 28.2k
4 votes

Check if the system is linear

[Note: it may happen that a teacher makes a oral mistake, that puzzles the audience. So here is an alternative explanation on this system being non-something] This system is, as far as Peter K., Matt ...
Laurent Duval's user avatar
4 votes
Accepted

Does $y[n] = x[n] \star (u[n]-u[n-2])$ have memory or is it memoryless?

The system $$y[n] = x[n] \star (u[n]-u[n-2])$$ where $u[n]$ is the unit step function, has memory. Indeed the system is equivalent to $$y[n] = x[n] \star ( \delta[n] + \delta[n-1] ) \implies y[n] = x[...
Fat32's user avatar
  • 28.2k
4 votes

As of 2019, which discrete nonlinear, time-invariant systems with memory are considered "easy" to model and identify?

The easiest is Urysohn adaptive filter: http://www.ezcodesample.com/UAF/UAF.html It can build nonlinear model by few lines of code. The theoretical details can be found here http://www.ezcodesample....
Andrew Polar's user avatar
4 votes

Stabilizing the inverse transform of a system

Like you mentionned, you cannot cancel a right-half-plane zero (or a zero outside the unit circle) by placing a pole on it. A unstable pole in your compensator will make the command of your controller ...
Ben's user avatar
  • 3,777
4 votes

Does the error in the impulse response accumulate when applying a step-input?

I don't know, if I am missing something here, but $e[n]$ and $e[n-1]$ are uncorrelated noise signals regarding the higher frequencies, but correlated regarding the low ones. By combining them, you ...
Max's user avatar
  • 2,323
4 votes

Transfer function and Laplace domain

First of all it's important to understand that this is all about linear and time-invariant (LTI) systems. Otherwise, you can't generally use a transfer function to characterize a system. So if you ...
Matt L.'s user avatar
  • 90k
4 votes
Accepted

is this signal is perodic?

A signal $e^{j(\omega t + \varphi)}$ has an angular frequency $\omega$ and period $T=2\pi/\omega$. The signal $x_1(t) = 7e^{j(5t + \pi/2)}$ thus has period $$T_1 = \frac{2\pi}{5}$$ Since $a^n = e^{n \...
Blackhole's user avatar
  • 155
3 votes
Accepted

Is it possible to estimate variance of noise for a step answer signal?

Hi: In order to estimate the variance, you need to have an underlying model for your signal. So, suppose that the model is $y_{t+1} = y_t + \epsilon_t$ $~\forall ~ t = 1,\ldots n $. assuming that $E(...
mark leeds's user avatar
  • 1,117
3 votes
Accepted

What is $H_2$ and $H_{\infty}$ control?

They are system norms, a metric that you can compare two different systems in terms of their generalized gain and spread. You can look these up no need for attaching physical motivation. You don't. ...
percusse's user avatar
  • 522
3 votes

Why use cross-spectral density to calculate frequency response?

in the audio biz, we call this the "Two-channel FFT". the cool thing about it is that you can measure the magnitude response of a room or something using music (that is decently broadbanded) as the ...
robert bristow-johnson's user avatar
3 votes

matched filtering in GSM

First, please read this answer of mine for a detailed description of matched filters for real-valued signals. In particular, note that what I called the matched filter for a signal $x(t)$ is a(n LTI) ...
Dilip Sarwate's user avatar
3 votes
Accepted

Showing a system is always controllable?

There's a very simple way to check controllability, indeed if you define the reachability matrix $$ R = \begin{pmatrix}B & AB & \dots & A^{n-1}B\end{pmatrix} $$ then the reachable subspace ...
LJSilver's user avatar
  • 768
3 votes
Accepted

Memorylessness of simple delay system

A system is memoryless if its output ($y(t)$) for each value of the independent variable ($t$ in this case) at a given time is dependent only on the input at that same time ($x(t)$). Every system ...
Tendero's user avatar
  • 5,020
3 votes

Implementation of Block LMS

As applesoup says in the comments the term $$ \mathbf{u}(kL+i)e(kL+i) $$ is a vector, not a single value (some integer). Why do you think it's a scalar? To answer your question: no, it's incorrect ...
Peter K.'s user avatar
  • 25.7k
3 votes

Protect an IIR filter from being reverse-engineered

Long answer: Let's model the information flow from your "hidden" IIR $X$ to your observable output $Y$ as $$ X \longrightarrow Y$$ Then, we call the amount of information you get per observation ...
Marcus Müller's user avatar
3 votes

What is the difference between a causal system and a system with memory?

A system is memoryless if its output at a given time is dependent only on the input at that same time (and potentially the time itself). The converse is called a system with memory ("memory ...
Laurent Duval's user avatar
3 votes

Transfer function and Laplace domain

(I was going to leave @Matt L.'s answer but, given the line of comments, I'll try, too) Let's say you have a 1st order lowpass prototype and you feed it a sine: $$\begin{align} &H(s)=\dfrac{1}{s+1}...
a concerned citizen's user avatar
3 votes

Why time invariant system in order to know any output for any input using the impulse response?

If the system is time-varying, its response to an impulse at $t=0$ might be very different from its response to an impulse at any other time instant. Hence, knowing only its response to $\delta(t)$ (i....
Matt L.'s user avatar
  • 90k
2 votes

System Identification with Periodic Signal Input

The point is, that you need to look at the influence of averaging on the final term in the equation $$ \hat{G}_N = [...] + \frac{V_N}{U_N}. $$ In case of periodic excitation $u$, the noise term $|...
snowflake's user avatar
  • 192
2 votes

System identification packages

SIDPAC is a freely available program from software.nasa.gov. It is targeted toward aircraft system id problems however the underlying methods are applicable to other problem types.
Charlie H's user avatar
2 votes

Is $y[n]=x[n] * x[n^2]$ invertible?

This system is not invertible and a single counter-example is sufficient to prove it. First express the signal $x[n^2]$ as $w[n]$ and then the output is $$y[n]= x[n] \star w[n]$$ Then let an example ...
Fat32's user avatar
  • 28.2k
2 votes
Accepted

Is $y[n]=x[n] * x[n^2]$ invertible?

The system is nonlinear (bilinear in $x$), with a nonlinear law (square) on indices. Odds are the system is not invertible. One can try to prove it in its full generally, or try to find a ...
Laurent Duval's user avatar

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