Questions tagged [causality]
The causality tag has no usage guidance.
55
questions
1
vote
1answer
19 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
56 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
36 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 ...
1
vote
2answers
58 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
37 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
15 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
41 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 ...
1
vote
2answers
61 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
106 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 ...
2
votes
1answer
45 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
578 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
51 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
$$\textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\...
1
vote
3answers
92 views
Is there any new scientific capability to build non-causal filters in real world?
According to this post:
In discrete-time systems, causality is a requirement only when
processing (filtering) signals in real time; i.e. when the
index nn corresponds to a physical time n×Tsn×...
0
votes
1answer
73 views
When is a discrete time transfer function unrealizable?
I don't understand why the following makes sense:
Given a second-order mass damper system in continuous time:
$H(s) = \frac{1}{ms^{2}+cs}$
Its inverse $H^{-1}(s)$ is unrealizable as a transfer ...
1
vote
1answer
48 views
System memory, causality, stability
im new into systems and im supposed to solve if the system has memory, us causal, linear, stationery, BIBO stable...The problem is i have never had experience with this type of system where the actual ...
2
votes
1answer
467 views
Initial Rest Condition for LCCDE causal LTI systems
I am self studying Alan Opennheim's course Signals and Systems. I am a math major and have no background in EE.
I understand that for a LCCDE system to be linear its auxiliary conditions must be 0.
...
-1
votes
1answer
92 views
Relation between causality and stability? [closed]
What is the relation between causality and stability of a system??To be stable,is it must for the system to be also causal? and if the system is not causal, will it not be stable?
or these two ...
5
votes
4answers
2k views
Is the first derivative operation on a signal a causal system?
Please help me sort this issue out.
Consider a system whose output $y(t)$ is the first derivative of the input signal $x(t)$.
We can write the first derivative of an input signal as follows:
$$y(t)...
0
votes
0answers
35 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 ...
0
votes
2answers
498 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
89 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
219 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
270 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 ...
0
votes
1answer
324 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
29 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
82 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 ...
0
votes
2answers
471 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
...
1
vote
2answers
1k views
What is a memory less system?
As far as I have grasped the concept is that if we are given the expression
$$y[n]=(2x[n]-x^2[n])^2\,,$$
it is a memory less system because even if we give negative values of $n$, we still get the ...
1
vote
1answer
592 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 ...
0
votes
1answer
2k views
How to conclude LTI, causality and BIBO stability of a system represented by a differential equation?
I have started to learn about systems represented by differential equations in Oppenheim's Signals & Systems, and I got really confused about it. I am trying to understand how I can show that a ...
2
votes
1answer
1k views
Precursor ISI - causality violation?
Today, in my lecture on intersymbol interference (ISI), there was a discussion on postcursor ISI, and precursor ISI. Postcursor ISI is caused by the past bits, whereas, precursor ISI is caused by the ...
5
votes
1answer
1k views
Does “improper” imply that a system cannot be stable and causal?
This answer and the comments in it made me wonder whether the following statement is true:
If a transfer function is improper, then that system cannot be causal and stable at the same time.
I had ...
7
votes
2answers
2k views
Physical Meaning of Negative Group Delay for causal LTI systems
I have implemented in Matlab (with minor variations) the example 5.1.2 "Illustration of Effects of Group Delay and Attenuation" I found in Alan Oppenheim's Discrete-Time Signal Processing 3rd edition. ...
0
votes
1answer
155 views
Time-invariance, causality and stability of $h(t)$ of four given systems
Question:
The impulse response functions of four linear systems $S_1,\ S_2,\ S_3,\ S_4$ are given respectively by
\begin{align}
h_1(t)&=1\\
h_2(t)&=u(t)\\
h_3(t)&=\frac{u(t)}{(t+1)}...
2
votes
2answers
2k views
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 ...
3
votes
1answer
648 views
For a system to be causal, number of finite zeros <= number of finite poles. Why?
I read in this pdf that for a system to be causal, the number of finite zeros must be no greater than number of finite poles. Why?
I know that for a system to be causal, $h[n]=0$ for all $n<0$. ...
4
votes
5answers
937 views
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 ...
2
votes
2answers
487 views
When inverting a transfer function, solving for the input using the output does the causality status change
suppose $y(n)=ax(n-1)+bx(n-2)+\dots$ ($y$ is the output and $x$ the input). What happens if I want to solve $x(n)$ from $y(n)$?
Z transform: $$Y(z)=G(z)X(z)\tag{1}$$
then $$X(z)=\frac{1}{G(z)...
1
vote
1answer
579 views
Hilbert transform properties
Here Its says Hilbert transform is a non-causal,linear,and time-invariant system
How can I prove it mathematically?
wikipedia says the input output relation like this $$\boxed{y(t)=\frac{1}{\pi}\...
3
votes
1answer
1k views
causality of the system $y[n] = x(2n)$
Can somebody please tell me why the system $y[n] = x(2n)$ is non-causal ?
I know that causal systems depend on the past and present values of input and
this system satisfies the condition. So why is ...
3
votes
2answers
91 views
whether the system is linear or not for the given problem
Given the system:
$$y(t)=x(t+1)+x(t−1)$$
is the system linear?
For a system to be a linear first it should satisfy zero input and zero output. How can we calculate output at 0 input if the system ...
0
votes
1answer
81 views
can $\frac{1}{H(z)}$ be causal and stable? [duplicate]
if we have linear phase FIR filter $H(z)$ which is causal and stable
can $\frac{1}{H(z)}$ be causal and stable ?
can it be causal without been stable ?
1
vote
1answer
1k views
Linearity, Causality and Stability of a System
Consider a system:
$$
y[n] = y[n-1] + u[n],
$$
where $y[n]$ is the output and $u[n]$ is the unit step function.
Is this system causal, linear, time-invariant and stable ?
My attempt at the ...
2
votes
1answer
3k views
Proof of Paley-Wiener criterion for causality
The Paley-Wiener criterion for causality is that $\displaystyle\int_{\mathbb{R}}\frac{A(\omega)}{1 + \omega^2}\mathrm{d}\omega$ exists and is finite, where $A(\omega) = \left|\mathcal{F}[f]\right|$ is ...
0
votes
1answer
288 views
How to analyse anti-causal discrete transfer function using matlab?
Consider a discrete transfer function that represents an anti causal filter such as a derivative filter:
$$H(z) = (-z^{-2} -2z^{-1} +2z +z^2) (1/8T)$$
Where T is the sampling period.
Normally in ...
1
vote
1answer
428 views
Definition of minimum-phase system
I saw a couple of definitions for minimum-phase in different textbooks and I'm trying to understand what the implication of each of them.
The first definition I saw was: An invertible system which ...
3
votes
2answers
451 views
Two real time signals convolving
This might be a stupid question but is it possible to convolve two real-time signals together? I know that generally for running convolution you have the IR and the block of the real time signal and ...
0
votes
1answer
1k views
Causality and ROC of a stable LTI system
So I am looking at a stable LTI system whose input is $x[n]$ and output is $y[n]$. The equation relating the two is here:
$$
y[n-1]-\frac{10}{3}y[n]+y[n+1]=x[n]
$$
I was able to compute its system ...
2
votes
1answer
609 views
Allpass Filters - Causal and Stable
So I have been learning about how to test systems for causality and stability but I am confused about the implications on their unit circle representation.
Would it be safe to say that a causal and ...
9
votes
1answer
873 views
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\limits_{-\infty}^{\infty} x(t) \, ...
