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13 votes
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Why are anticausal systems even defined?

Of course they don't exist. But we can stop time and use systems that would be non-causal if we hadn't stopped time. Stop time? Yes, just store your data and work offline / non-realtime. Or work on ...
Matt L.'s user avatar
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11 votes
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How can an impulse generate an output in the past time frame?

As mentioned in SakSath's answer a system with $h[n]\neq 0$ for $n<0$ is non-causal. Such a system cannot be implemented in real-time. However, you could use such a system for offline processing. ...
Matt L.'s user avatar
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11 votes
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Is there a relation between an analytic signal (signal processing) and an analytic function (complex analysis)?

There is a relationship between these two concepts. Let the complex function $f(z)$ be analytic on and inside a simple closed curve $C$ in the complex plane. Then Cauchy's integral formula states that ...
Matt L.'s user avatar
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10 votes
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Non-causality of fractional delays

It's not the delay itself that causes the total discrete-time system to be non-causal. In continuous time we simply have an impulse response $\delta(t-t_0)$, which is clearly causal for $t_0>0$. ...
Matt L.'s user avatar
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8 votes

Is the first derivative operation on a signal a causal system?

If the derivative exists at the given point, then it doesn't matter if you look (infinitesimally) into the future or into the past, you can do both, because both will give the same result: $$x'(t)=\...
Matt L.'s user avatar
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7 votes
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In the context of transfer functions, what is the relationship between the terms "proper", "causal", and "realizable"?

Causality is a necessary condition for realizability. Stability (or, at least, marginal stability) is also important for a system to be useful in practice. For linear time-invariant (LTI) systems, ...
Matt L.'s user avatar
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7 votes

Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?

Consider the identity system $y(t) = x(t)$. This system is LTI. If the input $x(t)$ is discontinuous, then the output $y(t)$ will be discontinuous too.
MBaz's user avatar
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7 votes

Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?

To add an even worse example to MBaz (best possible) counterexample: The derivative $\frac{\mathrm d}{\mathrm dt}$ is an LTI system. $f(t)=|t|$ is a continuous function. $\frac{\mathrm d}{\mathrm dt}(|...
Marcus Müller's user avatar
6 votes
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Why is $y(t)=x(t/2)$ a non-causal system?

Because for negative values of $t$ you have, for example, $y(-2) = x(-1)$ which depends on a future value of $x(t)$ at $t=-1$ for the current value of $y(t)$ at $t=-2$. Note that $t=-1$ represents a ...
Fat32's user avatar
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6 votes
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Why the frequency response plots (of causal filters) only show positive frequency?

This has absolutely nothing to do with causality. The frequency response of a real-valued filter (i.e., one with a real-valued impulse response) is (conjugate) symmetric, i.e., the negative ...
Matt L.'s user avatar
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6 votes
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Is this system causal or not?

Note that in this case you can see that the system is causal only from the given implementation. It's important to understand that you can't see it from the difference equation (if no initial ...
Matt L.'s user avatar
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5 votes
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causality of the system $y[n] = x(2n)$

No it does not satisfy the condition. Simply take an example: $$n = 1 \implies y[1] = x[2]$$ Hence the output value at the present time $n=1$ depends on a future value of the input at time $n=2$. ...
Fat32's user avatar
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5 votes
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Why can't a causal digital filter have an infinitely sharp transition between the passband and the stopband?

I don't have a concrete proof for this one. However, I can tell you this... Consider a perfect low pass filter. The time domain representation is a sinc. And for any system to have a sharp transition ...
Aaditya Ravindran's user avatar
5 votes

Why is $y(t)=x(t/2)$ a non-causal system?

HINT: Use a negative time $t$ to see that $y(t)$ depends on future input values.
Matt L.'s user avatar
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5 votes
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Is the first derivative operation on a signal a causal system?

Also consider the somewhat simpler "identity system", given a continuous signal $x(t)$: $$\begin{align}y(t) &= x(t)\tag{1}\\ &= \lim_{\Delta t\to0^-}x(t + \Delta t)\tag{2}\\ &= \lim_{\...
Olli Niemitalo's user avatar
5 votes

Non-causality of fractional delays

Just an expansion on Matt's great answer: you have stumbled into the "dirty little secret of sampling" :-) In order to sample without aliasing the signal has to be bandlimited. However, any ...
Hilmar's user avatar
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5 votes
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Why does causality imply that the system function is analytic?

New answer: I provide a new answer because I believe that this is a clearer and more direct way of explaining the relation between causality of the impulse response and analyticity of the ...
Matt L.'s user avatar
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4 votes
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What is the easiest, most straight-forward way to prove this about minimum-phase filters?

The Hilbert transform $\mathcal{H}\left\{f(\omega)\right\}$ with $$f(\omega)=-\frac12\log(1+\omega^2)\tag{1}$$ can be calculated in the following way. First, note that $$\frac{df(\omega)}{d\omega}=-...
Matt L.'s user avatar
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4 votes

Causal system and Physical Systems

The Paley-Wiener criterion defines a condition on the magnitude spectrum of a causal time-domain function. So if the Paley-Wiener criterion is satisfied for a given $A(\omega)=|H(\omega)|$, we know ...
Matt L.'s user avatar
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4 votes
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Signals and systems : why do we study causal signals?

An LTI system (or even a system that isn't L or TI) that is "causal" has a prayer of being realized in real time whereas an "acausal" system cannot ever be realized in real time because an acausal ...
robert bristow-johnson's user avatar
4 votes

How to analyse anti-causal discrete transfer function using matlab?

The transfer function $$H(z)=-z^{-2} -2z^{-1} +2z +z^2$$ can be written as $$\begin{align} H(z)&=z^2z^{-2}\left(-z^{-2} -2z^{-1} +2z +z^2\right)\\ &=z^2\left(-z^{-4} -2z^{-3} +2z^{-1} +1\right)...
msm's user avatar
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4 votes
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For a system to be causal, number of finite zeros <= number of finite poles. Why?

If the number of finite zeros is not greater than the number of finite poles then the transfer function is proper, i.e., the degree of the numerator polynomial is not greater than the degree of the ...
Matt L.'s user avatar
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4 votes

Why can't a causal digital filter have an infinitely sharp transition between the passband and the stopband?

This is three years later, but since I don't see the real answer posted here, I will post it. The correct answer is that if we are literally interpreting the original statement as a purely ...
Mike Battaglia's user avatar
4 votes

Why can't a causal digital filter have an infinitely sharp transition between the passband and the stopband?

My answer implicitly refers to ideal brickwall lowpass filters which do have infinetely sharp transition bands. For other possible interpretations, refer to other answers. In practice, neither analog, ...
Fat32's user avatar
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4 votes
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Does "improper" imply that a system cannot be stable and causal?

An improper system cannot be causal and stable. If the order of the numerator is greater than the order of the denominator, you'll always have at least one pole at infinity. Consequently, not all ...
Matt L.'s user avatar
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4 votes
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How to conclude LTI, causality and BIBO stability of a system represented by a differential equation?

I take your equation: $\frac{d^2y}{dt^2}-3\frac{dy}{dt}+2y(t)=x(t)$ Laplace transform will be: $ s^2Y(S) - 3sY(S) +2Y(s) = X(s) $ Now I can find transfer function: $H(s) \triangleq \frac{Y(s)}{X(s)}$...
Andrea's user avatar
  • 539
4 votes

What is a memoryless system?

Confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices". A strict memory-less system depends ...
Laurent Duval's user avatar
4 votes
Accepted

Realization of a filter based on its transfer function

A transfer function is called realizable if it can be implemented by a causal and stable system. The given frequency response is continuous and doesn't have any impulses, so the corresponding system ...
Matt L.'s user avatar
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4 votes

Relation between causality and stability?

They are independent of each other. Continuous systems: For stability, the ROC (region of convergence) must include the jw-axis of the s-plane. Causal systems have a ROC which is a right-sided plane,...
Axel Mancino's user avatar
4 votes

Confusion understanding causality?

The statement is not correct. In a causal system, the cause (i.e. input) does indeed precede (come before in time) the corresponding effect (output). The correct statement is the cause doesn't follow ...
Dsp guy sam's user avatar
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