Questions tagged [causality]
The causality tag has no usage guidance.
101
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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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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:
$$ \begin{align}
X(f) \triangleq \mathscr{F}\{x(t)\} &= \int\...
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9
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Physical Meaning of Negative Group Delay for causal LTI systems
I have implemented in Matlab (with minor variations) the example 5.1.2 "Illustration of Effects of Group Delay and Attenuation" I found in Alan Oppenheim's Discrete-Time Signal Processing 3rd edition. ...
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Is the first derivative operation on a signal a causal system?
Please help me sort this issue out.
Consider a system whose output $y(t)$ is the first derivative of the input signal $x(t)$.
We can write the first derivative of an input signal as follows:
$$y(t)...
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8
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1
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Causal system and Physical Systems
According to the Paley-Wiener criterion, a system is causal if satisfies:
$$\int\limits_{-\infty }^{+\infty }{\frac{\ln (|H(f)|)}{1+{{f}^{2}}}}df<\infty$$
So I want to know
This equation is ...
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7
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6
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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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6
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2
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402
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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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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 ...
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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 ...
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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 ...
- 142
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3
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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:
$$
\begin{cases}
w[k]+5w[k-1]+6w[k-2]=x[k] \\
y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3]
\end{cases}
$$...
- 145
4
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2
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504
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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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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 $X[k]$ ...
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4
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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 ...
4
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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 ...
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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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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 ...
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654
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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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2
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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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In the context of transfer functions, what is the relationship between the terms "proper", "causal", and "realizable"?
I am thinking about these terms in the context of linear control.
A transfer function is proper if the degree of the numerator is not greater than the degree of the denominator. I've read often that ...
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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 ...
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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 $n<0$. ...
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2
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177
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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 ...
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3
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1
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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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635
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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:
$$y(t) = \...
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2
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What characterizies 'causality' for a finite FFT?
Causality of a LTI transfer function $G(\tau)$ in the continuous time domain, i.e. for
$$y(t)=\int G(\tau)x(t-\tau)d\tau$$
is characterized by
$$G(\tau < 0) = 0$$
By the way, in the frequency ...
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Causal and Non-memoryless LTI sytems described by LCCDE
I was wondering about the nature of stable systems (in the BIBO sense) that are causal with memory for which we wish to represent them by LCCDE (if they may exist). How frequent do LCCDE exist such ...
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3
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Is there any new scientific capability to build non-causal filters in real world?
According to this post:
In discrete-time systems, causality is a requirement only when
processing (filtering) signals in real time; i.e. when the
index nn corresponds to a physical time n×Tsn×...
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What is the difference between a causal system and a system with memory?
As far as I know, memoryless systems are causal systems. But why aren't systems with memory necessarily causal?
Since the system with memory is affected by past input and current input, I think that ...
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Intuitive explanation of magnitude-phase-relationship for minimum phase filters
I know that, given the magnitude response $|H(e^{j \omega})|$ of a filter $H(z)$, it's minimum-phase response is given by
$$
\phi(\omega) = -\mathscr{H}\Big\{ \log(|H(e^{j \omega})|) \Big\} \ .
$$
I ...
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4
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549
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why we do pure delay to make causal fir filter?
Sometimes, we met Non-causal FIR filter problem like this picture
left is ifft of frequency response and right is time shifted fir filter to be causal filter
in noise cancellation problem, delay is ...
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When inverting a transfer function, solving for the input using the output does the causality status change
suppose $y(n)=ax(n-1)+bx(n-2)+\dots$ ($y$ is the output and $x$ the input). What happens if I want to solve $x(n)$ from $y(n)$?
Z transform: $$Y(z)=G(z)X(z)\tag{1}$$
then $$X(z)=\frac{1}{G(z)...
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2
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1
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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 ...
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1
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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
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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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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 ...
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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 ...
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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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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 ...
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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. ...
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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= ...
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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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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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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 ...
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3
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Signals and systems : why do we study causal signals?
Till now I have read that causal signals are right sided and anti-causal, left sided.
Why did we need to classify a signal with respect to its position?
What is it's physical interpretation?
...
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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 "...
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2
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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(...
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vote
1
answer
136
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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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2
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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 ...
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2
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5k
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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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