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Inverse of a causal and stable system

Consider a discrete-time causal and stable LTI system $S_1$​. The inverse system $S_2$​ is defined as the system that takes the output of $S_1$​ as its input and provides the input of $S_1$​ as its ...
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How to prove this system is not causal?

I set $x_1(t)=0$ and use the final rest property to get $y_1(t)=0$, and $y_2(t)=0$ for $t>1$. However, I cannot find general $y_2(t)$ for $x_2(t)$.
LSK's user avatar
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is this system linear? causal?

$$y(t) = \int_{t_0}^t u(\tau)\, d\tau + y(t_0)$$ I have trouble determining whether this system is causal or not and linear or not. I think this system is causal because it integrates input signals ...
karma123's user avatar
1 vote
1 answer
125 views

If the input of the system depends on the future outputs then is the system non-causal?

While I'm aware of the fact that causality implies that the present output is only dependent on present and past inputs, something that is bugging me is what if the input is dependent on future ...
Ahan Shetty's user avatar
2 votes
1 answer
198 views

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 ...
herrzinter's user avatar
12 votes
1 answer
1k views

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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4 votes
2 answers
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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, ...
David Cian's user avatar
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2 answers
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Condition for Causality

I found, as rule of thumb, that a system is causal and stable when it poles lies inside the unit circle. However, more generally we should argue with region of convergence here, like in this example ...
bilaljo's user avatar
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5 answers
788 views

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 ...
Jiro's user avatar
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2 answers
666 views

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 ...
Madavan Viswanathan's user avatar
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1 answer
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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 ...
Joako's user avatar
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1 answer
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Matlab command "iztrans"only applicable for causal signals? [closed]

Matlab command for inverse z transform iztransonly applicable for causal signals? or also valid for non causal signals? Actually i want to find inverse z transform ...
DSP_CS's user avatar
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Non-causality deepness of inverse system

Assume I have a FIR, stable and causal system. I want to know the deepness of non-causality on the inverse of my FIR system. It's obvious that the system is non-minimum-phase, since minimum-phase ...
mohammadsdtmnd's user avatar
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2 answers
110 views

Causality of an estimated filter

Assume $\tilde{h}(f)$ is a filter estimated by an algorithm for (room) impulse response estimation working in the frequency domain. Is there a way to assert if such filter is causal? Specifically, ...
Chutlhu's user avatar
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LTI system: can I infer the system is causal based only on the transfer function without the ROC?

Suppose we have an linear time-invariant (LTI) system which acts on discrete signals. Suppose someone tells us the transfer function is: $$H(z) = \frac{1}{z-2},$$ but doesn't specify the ROC. Now the ...
Algo's user avatar
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1 answer
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Using Zero-Phase Anti-Causal Filters in Real-Time Embedded Systems

Wanted to know the feasibility and usefulness of implementing Zero-Phase Anti-Causal filters such as those mentioned at this link in modern embedded signal processing applications given the ...
malik12's user avatar
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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 ...
AdamsK's user avatar
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1 answer
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Tell FIR part and IIR part of a signal apart

I have been trying to figure out one of the homework assignments for my DSP class, and have been spending quite a lot of time figuring out a particular problem. The solution to this problem was given ...
Meow _J's user avatar
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6 votes
2 answers
478 views

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 ...
Emm386's user avatar
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Acausal form of $Z^{-1}\left(\frac{1}{z-a}\right)$

We know that $Z^{-1}\left(\frac{z}{z-a}\right) = a^nu[n]$ if $|z| > |a|$. In addition, $Z^{-1}\left(\frac{1}{z-a}\right) = a^{n-1}u[n-1]$ if $|z| > |a|$. This is the delayed version of the first ...
sdkmlcngz's user avatar
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1 answer
249 views

What is causal inverse of a system?

Let's say that I have a system $H(z)$. What is causal inverse and how do I compute the causal inverse of $H(z)$?
Nathan Tyson's user avatar
2 votes
1 answer
430 views

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 ...
jvf's user avatar
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1 answer
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Prove that the filter is stable, causal and minimum phase

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. This system, as ...
Mark's user avatar
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4 votes
3 answers
592 views

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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2 answers
140 views

Sufficient conditions for invertibility of discrete LTI systems [duplicate]

Is $h[0] \neq 0$ a sufficient condition for the invertibility of a discrete, LTI, causal system? Can we get to similar results (i.e. get to some other sufficient condition(s)) for noncausal or ...
Dkpink's user avatar
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2 answers
290 views

Does causality imply linearity in a discrete system described by difference equations?

In my textbook, it is stated that for a discrete system, where the input and output are expressed by difference equations, to be causal, there needs to be initial rest. It is also stated that for the ...
Dkpink's user avatar
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2 votes
4 answers
681 views

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 ...
gg h's user avatar
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1 answer
158 views

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 ...
Crataegus's user avatar
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1 answer
409 views

Causality on an accumulator system

Can anybody explain why is this system not causal. $$T[x[n]] = \sum_{k=n_0}^{n} x[k]$$ How does it depend from future inputs when $n < n_0$. If $n < n_0$ then $T[x[n]]$ is zero because of ...
Derteck's user avatar
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1 vote
1 answer
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Expression of output for discrete time causal filters

I have a question about the expression of the output of a discrete time filter described by its impulse response $h(k)$. Looking at the defintion of a discrete filter with input $u(k)$ and output $y(k)...
Peter's user avatar
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2 votes
3 answers
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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 ...
Joon Woo Lee's user avatar
4 votes
2 answers
178 views

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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1 answer
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When is a LTI IIR $H(z)$ system minimum phase

EDIT: I failed to mention that the system's inverse also needs to be causal and stable. I cannot wrap my mind around on how when a system and its inverse are both causal and stable and LTI IIR it is ...
Nyquist-er's user avatar
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Stable and causal system

How many stable and causal systems with the same magnitude response are there? I know this relates to an all pass system for two rational transfer functions but am not sure about the specifics of this
Amanda Mironia's user avatar
3 votes
0 answers
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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 ...
SPARSE's user avatar
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0 answers
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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 ...
Peter K.'s user avatar
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1 vote
1 answer
219 views

Initial rest condition applied on $x(t)$ vs $h(t)$

Define the LTI system $\mathcal{H} : x\mapsto y$ Define the convolution for continuous-time system : $$ (x*h)(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)\;\text{d}\tau $$ The initial rest condition ...
B E I R U T's user avatar
4 votes
3 answers
2k views

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: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$...
uriyabsc's user avatar
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0 votes
2 answers
197 views

Non-causal FIR filter in the feedback loop

I have a feedback loop with a transfer function $H(z) = \sum_{i=0}^{L-1} h(i) z^{-i}$. Is there a way to make this FIR filter non-causal? If it was a feed-forward filter, we could simply do so by ...
dsp_guy2020's user avatar
2 votes
0 answers
364 views

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 ...
BandW's user avatar
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2 answers
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Determining Causality and Time-Invariance of a system

Consider the following system: $$y(t-1)=\int_{-\infty}^\infty x(𝜏)u(𝜏-t) d𝜏 $$ where $u(t)$ is the unit step function, which is zero for $t<0$ and equals $1$ for $t>0$. $(1)$ Is the system ...
BCompl's user avatar
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1 vote
1 answer
166 views

Why can you use the one-sided laplace transform to solve differential equation describing a causal LTI-system?

In an example, an equation describing a causal LTI-system is $$ (D^2 + 5D + 6) y(t) = (D+1) x(t) $$ where $y(t) = y_{zs}(t) + y_{zi}(t)$ and the initial conditions are $y(0^-) = 2, \dot{y}(0^-) = 1$. $...
DancingIceCream's user avatar
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0 answers
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Stability of $x(n) = A x(n-1)+b$

I am looking at the following system: $x(n) = A x(n-1) + b$ where x and b are vectors and A is a matrix. How can I derive the stability and causality conditions for such a system using Z transform? If ...
dsp_guy2020's user avatar
0 votes
1 answer
177 views

How does the intuitive notion of causality fit in with control systems?

Edit: By causality, in this question, I do not mean the traditional mathematical definition in the theory o signals and systems; I mean causality as in an intuitive 'what's moving/pushing what notion'....
Mohamad Hussein Naim's user avatar
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1 answer
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expression for the FT of the frequency response of a system

I am trying to find an expression for the Fourier Transform of the frequency response of the cascade system seen here: Here is my approach: $(-1)^n = (-1)^{-n}$ $v[n] = x[n]e^{j\pi n}$ $V(e^{jw}) = X(...
dnclem's user avatar
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1 answer
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impulse response of a causal LTI system

This is a difference equation to a causal LTI system: $y[n] = ay[n - 1] + x[n] - a^Nx[n - N]$ Where N is a positive integer. I need to determine the impulse response of the system, so I have the ...
dnclem's user avatar
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0 answers
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Discrete Time Systems with cosine()

I am trying to see if y[n] = [cos(πn)]x[n] is casual, stable, linear and shift-invariant. I came up with the solution that it is not stable since it is not "...
Jorge Juarez's user avatar
2 votes
1 answer
917 views

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. ...
Triceratops's user avatar
3 votes
1 answer
738 views

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) = \...
DarthCavader's user avatar
0 votes
1 answer
358 views

Determine causality and stability from given filter structure

I have the diagram above. I found the transfer function below from it; The question asks me to find out if the system is causal and stable, but didn't it have to indicate whether it was left-sided or ...
cem ekkazan's user avatar