# Questions tagged [causality]

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### Are systems considered causal if they depend on prediction of future inputs?

A causal system is a system whose output only depends on the present or the past inputs. But there are many systems that do a look-ahead prediction and involves that in the calculation. For example, ...
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### Inverse of a causal and stable system

Consider a discrete-time causal and stable LTI system $S_1$​. The inverse system $S_2$​ is defined as the system that takes the output of $S_1$​ as its input and provides the input of $S_1$​ as its ...
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### How to prove this system is not causal?

I set $x_1(t)=0$ and use the final rest property to get $y_1(t)=0$, and $y_2(t)=0$ for $t>1$. However, I cannot find general $y_2(t)$ for $x_2(t)$.
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### is this system linear? causal?

$$y(t) = \int_{t_0}^t u(\tau)\, d\tau + y(t_0)$$ I have trouble determining whether this system is causal or not and linear or not. I think this system is causal because it integrates input signals ...
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### If the input of the system depends on the future outputs then is the system non-causal?

While I'm aware of the fact that causality implies that the present output is only dependent on present and past inputs, something that is bugging me is what if the input is dependent on future ...
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### Intuitive explanation of magnitude-phase-relationship for minimum phase filters

I know that, given the magnitude response $|H(e^{j \omega})|$ of a filter $H(z)$, it's minimum-phase response is given by $$\phi(\omega) = -\mathscr{H}\Big\{ \log(|H(e^{j \omega})|) \Big\} \ .$$ I ...
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### Is there a relation between an analytic signal (signal processing) and an analytic function (complex analysis)?

In signal processing, we define an analytic signal as a complex-valued signal which has no frequency components for $\omega<0$. It can be shown that the real part and the imaginary part of an ...
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### Why does causality imply that the system function is analytic?

It is cited in multiple places that the fact that a filter is causal (i.e. the impulse response is zero for t < 0) implies that the system function is analytical. I couldn't find any proof of this, ...
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### Condition for Causality

I found, as rule of thumb, that a system is causal and stable when it poles lies inside the unit circle. However, more generally we should argue with region of convergence here, like in this example ...
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### Non-causality of fractional delays

Given a physical system (e.g., loudspeaker and microphone) with DA and AD converters. Playing a single pulse from the loudspeaker, I will most likely receive the pulse at the microphone with a ...
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### How can an impulse generate an output in the past time frame?

I am studying signal processing and currently doing signals & systems. While going through convolution and especially the impulse response , there are problems where LTI systems wherein the input ...
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### Does the Kramer-Kronig relations apply to this example $f(t) =\left(1-t^2\right)^4\cdot\theta(1-t^2)$?

Does the Kramer-Kronig relations apply to this example $f(t) =\left(1-t^2\right)^4\cdot\theta(1-t^2)$? with $\theta(t)$ is the Heaviside step function. I made a detailed related question here with ...
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### Matlab command "iztrans"only applicable for causal signals? [closed]

Matlab command for inverse z transform iztransonly applicable for causal signals? or also valid for non causal signals? Actually i want to find inverse z transform ...
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### Non-causality deepness of inverse system

Assume I have a FIR, stable and causal system. I want to know the deepness of non-causality on the inverse of my FIR system. It's obvious that the system is non-minimum-phase, since minimum-phase ...
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### Causality of an estimated filter

Assume $\tilde{h}(f)$ is a filter estimated by an algorithm for (room) impulse response estimation working in the frequency domain. Is there a way to assert if such filter is causal? Specifically, ...
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### LTI system: can I infer the system is causal based only on the transfer function without the ROC?

Suppose we have an linear time-invariant (LTI) system which acts on discrete signals. Suppose someone tells us the transfer function is: $$H(z) = \frac{1}{z-2},$$ but doesn't specify the ROC. Now the ...
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### Using Zero-Phase Anti-Causal Filters in Real-Time Embedded Systems

Wanted to know the feasibility and usefulness of implementing Zero-Phase Anti-Causal filters such as those mentioned at this link in modern embedded signal processing applications given the ...
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### Classification of a system

I am preparing for an examination and have a study guide that I feel has a couple of errors. The questions concern the classification of discrete time dynamical system. Here are the problems that I am ...
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1 vote
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### Tell FIR part and IIR part of a signal apart

I have been trying to figure out one of the homework assignments for my DSP class, and have been spending quite a lot of time figuring out a particular problem. The solution to this problem was given ...
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### Are allpass filters maximum-phase systems?

There are few notes online stating that an all-pass filter is a maximum phase filter (e.g., Link). The core of the claim is that an all-pass filter is a maximum phase filter since its zeros are ...
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### Acausal form of $Z^{-1}\left(\frac{1}{z-a}\right)$

We know that $Z^{-1}\left(\frac{z}{z-a}\right) = a^nu[n]$ if $|z| > |a|$. In addition, $Z^{-1}\left(\frac{1}{z-a}\right) = a^{n-1}u[n-1]$ if $|z| > |a|$. This is the delayed version of the first ...
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### What is causal inverse of a system?

Let's say that I have a system $H(z)$. What is causal inverse and how do I compute the causal inverse of $H(z)$?
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### How/why is the relative degree of a transfer function related to the causality of the system it represents?

A transfer function can be classified as strictly proper, proper or improper depending on its relative degree, i.e. the difference between the degree of the polynomial in the denominator and the ...
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### Prove that the filter is stable, causal and minimum phase

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. This system, as ...
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### Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?

Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions? I had this question when I saw this claim in my textbook: for ...
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### Sufficient conditions for invertibility of discrete LTI systems [duplicate]

Is $h[0] \neq 0$ a sufficient condition for the invertibility of a discrete, LTI, causal system? Can we get to similar results (i.e. get to some other sufficient condition(s)) for noncausal or ...
290 views

### Does causality imply linearity in a discrete system described by difference equations?

In my textbook, it is stated that for a discrete system, where the input and output are expressed by difference equations, to be causal, there needs to be initial rest. It is also stated that for the ...
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### why we do pure delay to make causal fir filter?

Sometimes, we met Non-causal FIR filter problem like this picture left is ifft of frequency response and right is time shifted fir filter to be causal filter in noise cancellation problem, delay is ...
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### Is the filter $1/(1-s)$ anti-causal?

The filter with the response function $$H(s) = \frac{1}{1 - s}$$ Produces a positive phase shift and a negative group delay for all frequencies Is it anti-causal? Is there a way to deduce such ...
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### Causality on an accumulator system

Can anybody explain why is this system not causal. $$T[x[n]] = \sum_{k=n_0}^{n} x[k]$$ How does it depend from future inputs when $n < n_0$. If $n < n_0$ then $T[x[n]]$ is zero because of ...
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### Stability of $x(n) = A x(n-1)+b$

I am looking at the following system: $x(n) = A x(n-1) + b$ where x and b are vectors and A is a matrix. How can I derive the stability and causality conditions for such a system using Z transform? If ...