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:
$$ \begin{align}
X(f) \triangleq \mathscr{F}\{x(t)\} &= \int\...
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What is a memoryless system?
As far as I have grasped the concept,
$$ y[n] = \left( 2 x[n] - x^2[n] \right)^2 $$
is a memoryless system because even if we give negative values of $n$, we still get the overall result in the ...
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Physical Meaning of Negative Group Delay for causal LTI systems
I have implemented in Matlab (with minor variations) the example 5.1.2 "Illustration of Effects of Group Delay and Attenuation" I found in Alan Oppenheim's Discrete-Time Signal Processing 3rd edition. ...
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Is there a relation between an analytic signal (signal processing) and an analytic function (complex analysis)?
In signal processing, we define an analytic signal as a complex-valued signal which has no frequency components for $\omega<0$. It can be shown that the real part and the imaginary part of an ...
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Causal system and Physical Systems
According to the Paley-Wiener criterion, a system is causal if satisfies:
$$\int\limits_{-\infty }^{+\infty }{\frac{\ln (|H(f)|)}{1+{{f}^{2}}}}df<\infty$$
So I want to know
This equation is ...
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Is the first derivative operation on a signal a causal system?
Please help me sort this issue out.
Consider a system whose output $y(t)$ is the first derivative of the input signal $x(t)$.
We can write the first derivative of an input signal as follows:
$$y(t)...
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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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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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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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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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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}\...
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