# Tag Info

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'...
• 90k
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 ...
• 30.6k
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 ...
• 51k
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 ...
• 31.9k
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 ...
• 25.7k

### 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 ...
• 301

### Recursive system

No, it can be rewritten as $y[n] = x[n]/2$. Basically, the output is the input divided by 2...
• 3,777

### 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 ...
• 28.2k

### 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 ...
• 31.9k
Accepted

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 $$y[n] = x[n] \star ( \delta[n] + \delta[n-1] ) \implies y[n] = x[... • 28.2k 4 votes ### As of 2019, which discrete nonlinear, time-invariant systems with memory are considered "easy" to model and identify? The easiest is Urysohn adaptive filter: http://www.ezcodesample.com/UAF/UAF.html It can build nonlinear model by few lines of code. The theoretical details can be found here http://www.ezcodesample.... • 301 4 votes ### Stabilizing the inverse transform of a system Like you mentionned, you cannot cancel a right-half-plane zero (or a zero outside the unit circle) by placing a pole on it. A unstable pole in your compensator will make the command of your controller ... • 3,777 4 votes ### Does the error in the impulse response accumulate when applying a step-input? I don't know, if I am missing something here, but e[n] and e[n-1] are uncorrelated noise signals regarding the higher frequencies, but correlated regarding the low ones. By combining them, you ... • 2,323 4 votes ### Transfer function and Laplace domain First of all it's important to understand that this is all about linear and time-invariant (LTI) systems. Otherwise, you can't generally use a transfer function to characterize a system. So if you ... • 90k 4 votes Accepted ### is this signal is perodic? A signal e^{j(\omega t + \varphi)} has an angular frequency \omega and period T=2\pi/\omega. The signal x_1(t) = 7e^{j(5t + \pi/2)} thus has period$$T_1 = \frac{2\pi}{5}$$Since a^n = e^{n \... • 155 3 votes Accepted ### Is it possible to estimate variance of noise for a step answer signal? Hi: In order to estimate the variance, you need to have an underlying model for your signal. So, suppose that the model is y_{t+1} = y_t + \epsilon_t ~\forall ~ t = 1,\ldots n . assuming that E(... • 1,117 3 votes Accepted ### What is H_2 and H_{\infty} control? They are system norms, a metric that you can compare two different systems in terms of their generalized gain and spread. You can look these up no need for attaching physical motivation. You don't. ... • 522 3 votes ### Why use cross-spectral density to calculate frequency response? in the audio biz, we call this the "Two-channel FFT". the cool thing about it is that you can measure the magnitude response of a room or something using music (that is decently broadbanded) as the ... 3 votes ### matched filtering in GSM First, please read this answer of mine for a detailed description of matched filters for real-valued signals. In particular, note that what I called the matched filter for a signal x(t) is a(n LTI) ... • 20.3k 3 votes Accepted ### Showing a system is always controllable? There's a very simple way to check controllability, indeed if you define the reachability matrix$$ R = \begin{pmatrix}B & AB & \dots & A^{n-1}B\end{pmatrix} $$then the reachable subspace ... • 768 3 votes Accepted ### Memorylessness of simple delay system A system is memoryless if its output (y(t)) for each value of the independent variable (t in this case) at a given time is dependent only on the input at that same time (x(t)). Every system ... • 5,020 3 votes ### Implementation of Block LMS As applesoup says in the comments the term$$ \mathbf{u}(kL+i)e(kL+i) $$is a vector, not a single value (some integer). Why do you think it's a scalar? To answer your question: no, it's incorrect ... • 25.7k 3 votes ### Protect an IIR filter from being reverse-engineered Long answer: Let's model the information flow from your "hidden" IIR X to your observable output Y as$$ X \longrightarrow Y$$Then, we call the amount of information you get per observation ... • 30.6k 3 votes ### What is the difference between a causal system and a system with memory? A system is memoryless if its output at a given time is dependent only on the input at that same time (and potentially the time itself). The converse is called a system with memory ("memory ... • 31.9k 3 votes ### Transfer function and Laplace domain (I was going to leave @Matt L.'s answer but, given the line of comments, I'll try, too) Let's say you have a 1st order lowpass prototype and you feed it a sine:$$\begin{align} &H(s)=\dfrac{1}{s+1}...
• 1,828
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....