Questions tagged [causality]
The causality tag has no usage guidance.
76
questions
2
votes
3answers
259 views
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 ...
4
votes
1answer
58 views
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 $X[k]$ ...
1
vote
1answer
56 views
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 ...
0
votes
0answers
27 views
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
3
votes
0answers
54 views
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 ...
2
votes
0answers
37 views
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 ...
1
vote
1answer
73 views
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 ...
4
votes
3answers
1k views
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:
$$
\begin{cases}
w[k]+5w[k-1]+6w[k-2]=x[k] \\
y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3]
\end{cases}
$$...
0
votes
2answers
56 views
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 ...
2
votes
0answers
86 views
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 ...
0
votes
2answers
133 views
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 ...
1
vote
1answer
64 views
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 $y(0^-) = 2, \dot{y}(0^-) = 1$.
$...
0
votes
0answers
38 views
Extrapolation of band-limited frequency data
I'm now studying "How to do accurate transform from band-limited frequency data specifically S-parameter data of high speed interconnect to the causal impulse response in time domain. There are ...
0
votes
0answers
19 views
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 ...
0
votes
1answer
67 views
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'....
0
votes
1answer
34 views
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(...
0
votes
1answer
157 views
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 ...
0
votes
0answers
32 views
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 "...
1
vote
1answer
307 views
Apply "non-causal" filter buffer-wise, a.k.a "soft real-time filtering"
I am dealing with digital filtering of signals, both offline and in real-time. Typical filtering purposes are highpass filter or bandpass filter.
So far I worked on prerecorded signals (e.g. ...
2
votes
1answer
220 views
Determining a system's causality using its impulse response
I have the following input-output relation for a system:
$$y(t) = Odd Part Of [x(t)]$$
My question is: Is the system causal?
What my approach has been:
I expressed $y(t)$ alternatively as:
$$y(t) = \...
0
votes
1answer
100 views
Determine causality and stability from given filter structure
I have the diagram above. I found the transfer function below from it;
The question asks me to find out if the system is causal and stable, but didn't it have to indicate whether it was left-sided or ...
1
vote
1answer
33 views
Linear response function for a system with derivative: $U=L \frac{d I}{dt}$, expressing $U=f(I)$
I have a super basic questions. I am a not really into signal processing (more about physics), but I would like to understand an aspect of linear response function (I think the question fits for this ...
2
votes
2answers
226 views
What characterizies 'causality' for a finite FFT?
Causality of a LTI transfer function $G(\tau)$ in the continuous time domain, i.e. for
$$y(t)=\int G(\tau)x(t-\tau)d\tau$$
is characterized by
$$G(\tau < 0) = 0$$
By the way, in the frequency ...
0
votes
3answers
42 views
Definition of causality of a system in Discrete Time Signal Processing [Alan V. Oppenheim]
The book states:
Causality implies that, if x1[n] = x2[n] for n <= n0, then y1[n] = y2[n] for n <= n0.
But isn't it always the case, that for same inputs we're getting same outputs except ...
2
votes
2answers
183 views
On the stability and causality of a discrete system
On MIT's open course a simple exercise with two questions is given. On the first part, they question about the properties of the following discrete system:
$$
y[n]=x[n]+0.5y[n−1]−2y[n−2]
$$
The ...
0
votes
1answer
205 views
How to check if h(n) is causal, stable? [closed]
I have $x(n)$ = {$4,-1,-3,1$} and $h(n)$ = {$2,1,3,5$}.
I would like to know how can I check whether
$h(n)$ is stable filter or not and
$h(n)$ is causal filter or not?
0
votes
1answer
38 views
How to find H(z) and H(k) from a given causal function
Consider the causal function,
$y[k] = 2x[k] - 40x[k - 1] + 10y[k - 1]$ $16y[k - 2]$;
where $y[k]$ is the output and $x[k]$ is the input. Assume that the system is initially at rest.
Please someone ...
0
votes
1answer
451 views
Initial rest condition for the linear constant-coefficient differential equations
Suppose that system has the input/output relation as follows
$$\sum_{k=0}^{N}a_k \frac{d^ky(t)}{dt^k} = \sum_{k=0}^{M}b_k \frac{d^kx(t)}{dt^k}$$
Where $a_k, b_k \in \mathbb{R}$.
Obviously we need ...
1
vote
2answers
116 views
Confusion understanding causality?
I already know the simple definition that causal system is the one that does not depend on future values of input but today i was confused as i came across a new definition of causality after reading "...
1
vote
1answer
253 views
Real-valued DTFT
Now this is a simple question, but I still ask it for clarification:
I know that an even signal $$h[n] = h[-n]$$ results in a real-valued DTFT (we have proven that in class). Now my question is the ...
5
votes
1answer
177 views
What are the properties of continuous-time improper systems?
I am trying to better understand the properties of improper systems $H(s) = \frac{b(s)}{a(s)}$, for which the order of the numerator $b(s)$ is greater than the order of the denominator $a(s)$ (in the ...
3
votes
4answers
657 views
Why are anticausal systems even defined?
I guess the same question is usually asked for complex numbers too, but the fact is that complex numbers are used all the time practically. However, at least on a quick google search, I couldn't find ...
0
votes
1answer
128 views
Relationship between real and imaginary part of a real-valued and causal system
I have one question about the real part of a real-valued and causal system with the imaginary part of its Fourier transform given by
$$\textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\...
1
vote
3answers
191 views
Is there any new scientific capability to build non-causal filters in real world?
According to this post:
In discrete-time systems, causality is a requirement only when
processing (filtering) signals in real time; i.e. when the
index nn corresponds to a physical time n×Tsn×...
0
votes
1answer
150 views
When is a discrete time transfer function unrealizable?
I don't understand why the following makes sense:
Given a second-order mass damper system in continuous time:
$H(s) = \frac{1}{ms^{2}+cs}$
Its inverse $H^{-1}(s)$ is unrealizable as a transfer ...
1
vote
1answer
112 views
System memory, causality, stability
im new into systems and im supposed to solve if the system has memory, us causal, linear, stationery, BIBO stable...The problem is i have never had experience with this type of system where the actual ...
2
votes
3answers
2k views
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 ...
-1
votes
1answer
200 views
Relation between causality and stability? [closed]
What is the relation between causality and stability of a system??To be stable,is it must for the system to be also causal? and if the system is not causal, will it not be stable?
or these two ...
6
votes
4answers
4k views
Is the first derivative operation on a signal a causal system?
Please help me sort this issue out.
Consider a system whose output $y(t)$ is the first derivative of the input signal $x(t)$.
We can write the first derivative of an input signal as follows:
$$y(t)...
0
votes
0answers
53 views
Causal bandpass using fft?
I would like to take a time series of several spikes or narrow Gaussians and bandpass using an ift/ifft together with a frequency domain mask to create a series containing band-limited spikes. This is ...
1
vote
2answers
2k views
Z transform - Inverse System function - Why number of poles and zeros myst be equal?
I know that if a system is causal then the system function H(z) must have :
a) a ROC that spans from the exterior of the most distant pole and
b) the number of zeros must not be greater than the ...
1
vote
0answers
321 views
Region of convergence of transfer function
I posted this question Mathematics SE and got no answer so I have posted it here.
I learned in my signal processing class that an LTI system can be defined using a linear constant coefficient ...
2
votes
1answer
447 views
Causal LTI system having exponential input
I know that for an LTI system having complex exponential input,
i.e, $x(t)=\exp(j w_o t)$ & $h(t) \to $ LTI System ;
then, its output { $y(t) \} =M \exp(j w_o t + \phi)$ , where $M= |H(j w)|_{|w= ...
0
votes
1answer
551 views
Why the frequency response plots (of causal filters) only show positive frequency?
Take an example of the below plot for an LPF (Source : WikiPedia)
The plot starts from $0$. We know that the fourier transform of any signal brings in negative frequencies due to complex exponentials ...
1
vote
1answer
426 views
System that has derivative of input is non causal
Consider a system $y(t) = \dot{x}(t)$ where $y$ is the output and $x$ is the input. Given an initial condition $x_0$ and two inputs $x_1$ and $x_2$ such that $$x_1(t)=x_2(t) , 0 \le t < t_0$$ the ...
0
votes
1answer
33 views
Causality of the given system
I am given the following discrete system
$$y[n]=x[-n]$$
where
$$x[n]=n+3$$.
Now from what I understand, since
$$y[n]=x[-n]$$
therefor the system is causal as the output is depending on the ...
0
votes
1answer
118 views
Finding the transfer function of a discrete signal described by two equations
A discrete time system is described by the following system of equations.
$$q[n] = \big(x[n]-\frac k4q[n-1]\big)$$
$$y[n] = \big(q[n]-\frac k3q[n-1]\big)$$
Find the systen function and then find the ...
1
vote
2answers
1k views
Realization of a filter based on its transfer function
How can we check whether the filter is realizable given its transfer function and What are the parameters the realization depends on?
Here is an example:
Show that a filter with transfer function
$H(...
1
vote
2answers
2k views
What is a memoryless system?
As far as I have grasped the concept,
$$ y[n] = \left( 2 x[n] - x^2[n] \right)^2 $$
is a memoryless system because even if we give negative values of $n$, we still get the overall result in the ...
1
vote
1answer
1k views
Impulse response of a causal system from transfer function in z-domain
The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$
I need to find the impulse response h[n] of a causal system with x[n] as unit impulse.
I have tried to find the impulse response by the following ...
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