# Tag Info

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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't depend on future input values), but a causal system doesn't need to be memoryless (because it may depend on past input or output values). The system $$y[n]=x[... 7 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 an arbitrarily long time, or add up observations), they will get an output, and can through the magic of correlation get the impulse response. 6 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 that if you want to identify your system with the impulse response h[n], you feed the sweep sine signal s[n] into it and record the output. Obviously output ... 5 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 affine in x[n] (and, therefore not linear) because of the bx[n-3] offset. On this site, we tend to go with the system definition rather than split hairs about ... 4 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 filtering is required to retrieve an estimate of the original signal that went through an unknown linear system. Basically, we have a signal which went through an ... 4 No, it can be rewritten as y[n] = x[n]/2. Basically, the output is the input divided by 2... 4 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 try counterexamples, based on your intuition. I don't really understand the motivation behind the second group of equations, or why b gets multiplied by \... 4 [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 L. and I know, nicely linear. You already did the computations. With a little more work, among classical properties, it is also time-invariant, causal, stable. ... 4 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[n] + x[n-1]$$and as it's clear from the given I/O relationship, the current value of the output y[n], depends on the values input x[n] at other times ... 4 Like you mentionned, you cannot cancel a right-half-plane zero (or a zero outside the unit circle) by placing a pole on it. A unstable pole in your compensator will make the command of your controller unbounded (i.e. it will reach infinity). There are no ways to cancel a right-half-plane zero. It's sometimes possible to "remove" a right-half-plane zero by ... 3 A system is memoryless if its output (y(t)) for each value of the independent variable (t in this case) at a given time is dependent only on the input at that same time (x(t)). Every system that consists of a delay (like the one in your example) or an accumulator, for example, are systems with memory. This can be seen just by replacing t by some ... 3 If the sensor is linear and invariant in time (an LTI system for linear and time-invariant), the output to a sine should be a sine with the same frequency, and a different phase and amplitude. Assuming that you will only probe the sensorin its linearity range (e.g. outside saturation), and that you only have access to the magnitude of the output sine, you ... 3 Knowing the amplitude (and phase) for several frequencies allows you to fit a model with as many parameters, hoping the system is linear. With little information you cannot observe the whole system behavior accurately, but just a simplified model. This might be enough for your purpose. Knowing the internal system structure should help you select an ... 3 There's a very simple way to check controllability, indeed if you define the reachability matrix$$ R = \begin{pmatrix}B & AB & \dots & A^{n-1}B\end{pmatrix} $$then the reachable subspace is the image of R. Hence to check complete controllability you just have to check that R is full rank. First, I think there's an error in the question, B ... 3 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 include u(n) in \theta, since it's defined by p. So you compute \frac{\partial Q}{\partial\theta}=0. Solving for \theta, and this is your new \theta ... 3 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 have all the poles and zeros of the transfer function within the unit circle. 2) An inverse filter of a filter with transfer function H(z) is a filter G(z) ... 3 conceptually, any driving signal with bandwidth that covers the maximum expected bandwidth of the system being identified is sufficient. you drive input and synchronously measure input and output, use the FFT to compute the spectra of both input and output, divide the output spectrum by the input spectrum, inverse FFT the resulting spectrum and you have the ... 3 The Periodogram implicitly uses a window to get an idea of the spectrum. Implicitly this is either a rectangular window, with frequency response which is like \dfrac{\sin(\omega n)}{N\sin(\omega)}, or a triangular window (N-k)/N. Roughly, the variance of the periodogram is the square of the Fourier transform multiplied by the square of the window. Note ... 3 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) filter with impulse response h(t) = x(-t) which is better described as the time-reversed signal rather than the "inverse" of the impulse response as you call ... 3 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. They are for assesing and using in the optimization programs. Yes, but only if you know what you are doing. Can be. But again, they are for assessment and ... 3 Output of a memoryless system depends only on the current input value and therefore every memoryless system is also causal; since a causal system's output cannot depend on the future input values. The converse in general is not true; causal systems can be memoryless as well as can exhibit memory (if their outputs depend on the past input values in addition ... 3 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 the *mutual information $I(X;Y)$; that information is the reduction of uncertainty about $X$ to be achieved by observing $Y$. We call the expected uncertainty ...

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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 Urysohn followed by static nonlinearity is a model of any deterministic dynamic object, it maps any given input to any provided output. I obtained Ph.D. in ...

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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 system" or "non-memoryless"): it can use past or future information. A causal system only on past inputs and outputs. Nota: the notion of "future&...

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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.

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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 expectations, because in practice expectations are usually approximated by time averages (hence 'smoothing'). If you have another method for computing these ...

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The answer to this (and your other similar question) is most likely found in the somewhat unusual notation used for the system. In ordinary terms, if you just take your system as a map between input and output signal, then you're absolutely right, it would not be time invariant. However, Proakis defines the system as a map from an input signal and a time ...

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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 $S_1(x(t+1)) = S_1(x(t)) = y(t)$. For $S_2$, the two bounds moving at the same time are promising, and a standard variable change shows the time invariance.

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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://www.cs.berkeley.edu/~jordan/papers/lindsten-etal-sysid12.pdf Q2: PBRS: https://en.wikipedia.org/wiki/Pseudorandom_binary_sequence. There is a lot of ...

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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 zero-state response is the response of a system to an input signal given that the initial state of the system is zero. The zero-input response is the output of the ...

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