Questions tagged [causality]
The causality tag has no usage guidance.
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What is the easiest, most straight-forward way to prove this about minimum-phase filters?
Using the "unitary" or "ordinary frequency" or "Hz" convention for the continuous Fourier Transform:
$$ \begin{align}
X(f) \triangleq \mathscr{F}\{x(t)\} &= \int\...
2
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1
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Intuitive explanation of magnitude-phase-relationship for minimum phase filters
I know that, given the magnitude response $|H(e^{j \omega})|$ of a filter $H(z)$, it's minimum-phase response is given by
$$
\phi(\omega) = -\mathscr{H}\Big\{ \log(|H(e^{j \omega})|) \Big\} \ .
$$
I ...
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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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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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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 ...
- 88.8k
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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 ...
3
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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 ...
3
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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 ...
- 88.8k
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One Sided Waveforms in Discrete Time and Frequency?
Consider a discrete time waveform $x[n]$ with $n \in [0...N-1]$ that is zero for all samples $n > N/2$ and non-zero elsewhere. Is there a waveform such that its Discrete Fourier Transform $X[k]$ ...
- 13.5k
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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, ...
- 48.8k
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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},$$ but doesn't specify the ROC. Now the ...
- 11.8k
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Using Zero-Phase Anti-Causal Filters in Real-Time Embedded Systems
Wanted to know the feasibility and usefulness of implementing Zero-Phase Anti-Causal filters such as those mentioned at this link in modern embedded signal processing applications given the ...
- 11.8k
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Classification of a system
I am preparing for an examination and have a study guide that I feel has a couple of errors. The questions concern the classification of discrete time dynamical system. Here are the problems that I am ...
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Tell FIR part and IIR part of a signal apart
I have been trying to figure out one of the homework assignments for my DSP class, and have been spending quite a lot of time figuring out a particular problem. The solution to this problem was given ...
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Are allpass filters maximum-phase systems?
There are few notes online stating that an all-pass filter is a maximum phase filter (e.g., Link). The core of the claim is that an all-pass filter is a maximum phase filter since its zeros are ...
- 88.8k
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Acausal form of $Z^{-1}\left(\frac{1}{z-a}\right)$
We know that $Z^{-1}\left(\frac{z}{z-a}\right) = a^nu[n]$ if $|z| > |a|$.
In addition, $Z^{-1}\left(\frac{1}{z-a}\right) = a^{n-1}u[n-1]$ if $|z| > |a|$. This is the delayed version of the first ...
CommunityBot
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What is a memoryless system?
As far as I have grasped the concept,
$$ y[n] = \left( 2 x[n] - x^2[n] \right)^2 $$
is a memoryless system because even if we give negative values of $n$, we still get the overall result in the ...
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What is causal inverse of a system?
Let's say that I have a system $H(z)$. What is causal inverse and how do I compute the causal inverse of $H(z)$?
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How/why is the relative degree of a transfer function related to the causality of the system it represents?
A transfer function can be classified as strictly proper, proper or improper depending on its relative degree, i.e. the difference between the degree of the polynomial in the denominator and the ...
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Prove that the filter is stable, causal and minimum phase
I have a system which has the following transfer function
$$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$
where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$.
This system, as ...
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What are the properties of continuous-time improper systems?
I am trying to better understand the properties of improper systems $H(s) = \frac{b(s)}{a(s)}$, for which the order of the numerator $b(s)$ is greater than the order of the denominator $a(s)$ (in the ...
CommunityBot
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Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?
Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?
I had this question when I saw this claim in my textbook:
for ...
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Sufficient conditions for invertibility of discrete LTI systems [duplicate]
Is $h[0] \neq 0$ a sufficient condition for the invertibility of a discrete, LTI, causal system? Can we get to similar results (i.e. get to some other sufficient condition(s)) for noncausal or ...
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Does causality imply linearity in a discrete system described by difference equations?
In my textbook, it is stated that for a discrete system, where the input and output are expressed by difference equations, to be causal, there needs to be initial rest. It is also stated that for the ...
- 11.8k
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why we do pure delay to make causal fir filter?
Sometimes, we met Non-causal FIR filter problem like this picture
left is ifft of frequency response and right is time shifted fir filter to be causal filter
in noise cancellation problem, delay is ...
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Is the filter $1/(1-s)$ anti-causal?
The filter with the response function
$$
H(s) = \frac{1}{1 - s}
$$
Produces a positive phase shift and a negative group delay for all frequencies
Is it anti-causal? Is there a way to deduce such ...
- 48.8k
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Causality on an accumulator system
Can anybody explain why is this system not causal.
$$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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Expression of output for discrete time causal filters
I have a question about the expression of the output of a discrete time filter described by its impulse response $h(k)$. Looking at the defintion of a discrete filter with input $u(k)$ and output $y(k)...
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Stability of filters with negative phase delay, group delay, and positive phase
Lets assume I have an IIR filter with :
bz = [1.0195 0 0];
az = [1 0.0166 0.0020];
fvtool(bz,az)
The filter is stable as i can see.
If you check the phase delay ...
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What is the difference between a causal system and a system with memory?
As far as I know, memoryless systems are causal systems. But why aren't systems with memory necessarily causal?
Since the system with memory is affected by past input and current input, I think that ...
- 88.8k
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When is a LTI IIR $H(z)$ system minimum phase
EDIT: I failed to mention that the system's inverse also needs to be causal and stable.
I cannot wrap my mind around on how when a system and its inverse are both causal and stable and LTI IIR it is ...
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Initial Rest Condition for LCCDE causal LTI systems
I am self studying Alan Opennheim's course Signals and Systems. I am a math major and have no background in EE.
I understand that for a linear constant-coefficient difference equation (LCCDE) system ...
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Stable and causal system
How many stable and causal systems with the same magnitude response are there?
I know this relates to an all pass system for two rational transfer functions but am not sure about the specifics of this
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Causal and Non-memoryless LTI sytems described by LCCDE
I was wondering about the nature of stable systems (in the BIBO sense) that are causal with memory for which we wish to represent them by LCCDE (if they may exist). How frequent do LCCDE exist such ...
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Why is $y(t)=x(t/2)$ a non-causal system?
I was going through my signal and system notes.they say $y(t)=x(t/2)$ is a non causal system? As non causal system depend on future inputs. how $t=t/2$ is future value of time? i could not understand ...
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How to determine which measurements cause which?
Suppose I have two sequences of measurements, $x_1[n]$ and $x_2[n]$ for $0 \le n \le N-1$.
How do I determine if there is a causal relationship between the two?
My first thought was, well... I can ...
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Initial rest condition applied on $x(t)$ vs $h(t)$
Define the LTI system $\mathcal{H} : x\mapsto y$
Define the convolution for continuous-time system :
$$
(x*h)(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)\;\text{d}\tau
$$
The initial rest condition ...
- 88.8k
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Is this system causal or not?
My efforts of solving this question are below.
I came to a conclusion that this system is causal, since:
$$
\begin{cases}
w[k]+5w[k-1]+6w[k-2]=x[k] \\
y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3]
\end{cases}
$$...
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Non-causal FIR filter in the feedback loop
I have a feedback loop with a transfer function $H(z) = \sum_{i=0}^{L-1} h(i) z^{-i}$. Is there a way to make this FIR filter non-causal? If it was a feed-forward filter, we could simply do so by ...
- 11.8k
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Why can't a causal digital filter have an infinitely sharp transition between the passband and the stopband?
In DSP book by Proakis and as well as in this pdf, it is mentioned that practical causal digital filters cannot have an infinitely sharp transition from Pass-band to Stop-band. Why is it so? Can you ...
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Determining Causality and Time-Invariance of a system
Consider the following system:
$$y(t-1)=\int_{-\infty}^\infty x(𝜏)u(𝜏-t) d𝜏 $$
where $u(t)$ is the unit step function, which is zero for $t<0$ and equals $1$ for $t>0$.
$(1)$ Is the system ...
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Why can you use the one-sided laplace transform to solve differential equation describing a causal LTI-system?
In an example, an equation describing a causal LTI-system is
$$
(D^2 + 5D + 6) y(t) = (D+1) x(t)
$$
where $y(t) = y_{zs}(t) + y_{zi}(t)$ and the initial conditions are $y(0^-) = 2, \dot{y}(0^-) = 1$.
$...
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How does the intuitive notion of causality fit in with control systems?
Edit: By causality, in this question, I do not mean the traditional mathematical definition in the theory o signals and systems; I mean causality as in an intuitive 'what's moving/pushing what notion'....
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Relationship between real and imaginary part of a real-valued and causal system
I have one question about the real part of a real-valued and causal system with the imaginary part of its Fourier transform given by
$$\textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\...
CommunityBot
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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 ...
- 15
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expression for the FT of the frequency response of a system
I am trying to find an expression for the Fourier Transform of the frequency response of the cascade system seen here:
Here is my approach:
$(-1)^n = (-1)^{-n}$
$v[n] = x[n]e^{j\pi n}$
$V(e^{jw}) = X(...
- 3,012
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impulse response of a causal LTI system
This is a difference equation to a causal LTI system:
$y[n] = ay[n - 1] + x[n] - a^Nx[n - N]$
Where N is a positive integer. I need to determine the impulse response of the system, so I have the ...
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Discrete Time Systems with cosine()
I am trying to see if
y[n] = [cos(πn)]x[n]
is casual, stable, linear and shift-invariant.
I came up with the solution that it is not stable since it is not "...
