Questions tagged [causality]

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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\...
robert bristow-johnson's user avatar
1 vote
2 answers

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 ...
Ahmad's user avatar
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9 votes
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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. ...
VMMF's user avatar
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12 votes
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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 ...
Matt L.'s user avatar
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8 votes
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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 ...
Ehsan Zakeri's user avatar
8 votes
4 answers

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)...
Nishanth Rao's user avatar
4 votes
3 answers

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 ...
HappyFace's user avatar
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4 votes
2 answers

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 $X[k]$ ...
Dan Boschen's user avatar
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3 votes
2 answers

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 ...
oliver's user avatar
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3 votes
1 answer

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 ...
Max's user avatar
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1 vote
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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}\...
Rohit's user avatar
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