8 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'...
user avatar
  • 79.2k
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 ...
user avatar
6 votes
Accepted

Am i performing Sinesweep correctly?

The theory behind sweep-sine measurements of LTI systems requires a signal with constantly changing the frequency. You cannot simply playback few tones - the whole frequency range is necessary. So ...
user avatar
  • 10.4k
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 ...
user avatar
  • 21.7k
5 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 ...
user avatar
  • 36.1k
4 votes

Conceptual questions from signal processing

Batman has given a great answer. You need to go through the recommended book in order to understand the concepts mentioned. Let me try to simplify it. BIG PICTURE: De-convolution or inverse ...
user avatar
  • 725
4 votes

Recursive system

No, it can be rewritten as $y[n] = x[n]/2$. Basically, the output is the input divided by 2...
user avatar
  • 3,544
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 ...
user avatar
  • 26.6k
4 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 ...
user avatar
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 ...
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[...
user avatar
  • 26.6k
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 ...
user avatar
  • 3,544
3 votes
Accepted

Expectation maximization of moving average with binary source input

I think your E-step is correct(only one term missing in the last expression: $-N\ln\sigma_w$ ). To obtain the M-step you have to differentiate with respect to all your parameters. You don't have to ...
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 ...
user avatar
  • 738
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) ...
user avatar
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 ...
user avatar
  • 4,842
3 votes

System identification only using sine input?

If the sensor is linear and invariant in time (an LTI system for linear and time-invariant), the output to a sine should be a sine with the same frequency, and a different phase and amplitude. ...
user avatar
3 votes
Accepted

Conceptual questions from signal processing

We will be talking about linear time-invariant systems. 1) A minimum phase filter is one which is causal and stable and its inverse is causal and stable. In the case of a discrete time system, you ...
user avatar
  • 1,071
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. ...
user avatar
  • 502
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 ...
user avatar
3 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 ...
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 ...
user avatar
3 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 ...
user avatar
  • 1,619
2 votes
Accepted

Natural, Forced and Total System Response - Time domain Analysis of DT

First of all, many textbooks use the following definition (but see this answer for a different one): zero-state response (ZSR) = forced response zero-input response (ZIR) = natural response The ...
user avatar
  • 79.2k
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.
user avatar
2 votes
Accepted

System Identification: smoothing in E-step of EM algorithm

The result of the $M$-step is expressed in terms of the matrices $\mathbf{P}_n^2$ and the vectors $\mathbf{x}_n^s$. These quantities are defined as expectations. Smoothing is used to compute these ...
user avatar
  • 79.2k
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 $|...
user avatar
  • 192
2 votes
Accepted

Determining if a system involving integrals is time varying or time-invariant

The fixed bound at 0 in $\int_0^t$ indeed suggests a time-variance.You only need a counter-example for $S_1$, like the constant $x(t) = 1$. $y(t+1) = t+1$, while $S_1(x(t+1)) = S_1(x(t)) = y(t)$. ...
user avatar
2 votes
Accepted

What is the estimator used in this paper for system identification?

Interesting paper! Q1: yes, seems like OLS, non-blind. Usually OLS is non-blind. Some sort of regulated least squares can be used in a bayesian ML-setting, blind. This paper looks interesting: http://...
user avatar

Only top scored, non community-wiki answers of a minimum length are eligible