Questions tagged [causality]

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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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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 ...
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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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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 ...
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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 ...
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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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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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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 ...
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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)...
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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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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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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 ...
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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
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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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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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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 ...
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4 votes
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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: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$...
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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 ...
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2 votes
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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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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 ...
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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 $y(0^-) = 2, \dot{y}(0^-) = 1$. $...
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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 ...
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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'....
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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(...
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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 ...
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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 "...
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1 vote
1 answer
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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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2 votes
1 answer
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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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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 ...
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1 vote
1 answer
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Linear response function for a system with derivative: $U=L \frac{d I}{dt}$, expressing $U=f(I)$

I have a super basic questions. I am a not really into signal processing (more about physics), but I would like to understand an aspect of linear response function (I think the question fits for this ...
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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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Definition of causality of a system in Discrete Time Signal Processing [Alan V. Oppenheim]

The book states: Causality implies that, if x1[n] = x2[n] for n <= n0, then y1[n] = y2[n] for n <= n0. But isn't it always the case, that for same inputs we're getting same outputs except ...
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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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How to check if h(n) is causal, stable? [closed]

I have $x(n)$ = {$4,-1,-3,1$} and $h(n)$ = {$2,1,3,5$}. I would like to know how can I check whether $h(n)$ is stable filter or not and $h(n)$ is causal filter or not?
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How to find H(z) and H(k) from a given causal function

Consider the causal function, $y[k] = 2x[k] - 40x[k - 1] + 10y[k - 1]$ 􀀀 $16y[k - 2]$; where $y[k]$ is the output and $x[k]$ is the input. Assume that the system is initially at rest. Please someone ...
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2 votes
1 answer
682 views

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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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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1 vote
1 answer
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Real-valued DTFT

Now this is a simple question, but I still ask it for clarification: I know that an even signal $$h[n] = h[-n]$$ results in a real-valued DTFT (we have proven that in class). Now my question is the ...
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5 votes
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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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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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Relationship between real and imaginary part of a real-valued and causal system

I have one question about the real part of a real-valued and causal system with the imaginary part of its Fourier transform given by $$\textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\...
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2 votes
3 answers
274 views

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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0 votes
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When is a discrete time transfer function unrealizable?

I don't understand why the following makes sense: Given a second-order mass damper system in continuous time: $H(s) = \frac{1}{ms^{2}+cs}$ Its inverse $H^{-1}(s)$ is unrealizable as a transfer ...
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System memory, causality, stability

im new into systems and im supposed to solve if the system has memory, us causal, linear, stationery, BIBO stable...The problem is i have never had experience with this type of system where the actual ...
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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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Relation between causality and stability? [closed]

What is the relation between causality and stability of a system??To be stable,is it must for the system to be also causal? and if the system is not causal, will it not be stable? or these two ...
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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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Causal bandpass using fft?

I would like to take a time series of several spikes or narrow Gaussians and bandpass using an ift/ifft together with a frequency domain mask to create a series containing band-limited spikes. This is ...
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1 vote
2 answers
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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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Region of convergence of transfer function

I posted this question Mathematics SE and got no answer so I have posted it here. I learned in my signal processing class that an LTI system can be defined using a linear constant coefficient ...
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