# Questions tagged [causality]

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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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### 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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### 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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### 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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### 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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### 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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1 vote
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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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### Impulse response of a causal system from transfer function in z-domain

The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$ I need to find the impulse response h[n] of a causal system with x[n] as unit impulse. I have tried to find the impulse response by the following ...
1 vote
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### How to conclude LTI, causality and BIBO stability of a system represented by a differential equation?

I have started to learn about systems represented by differential equations in Oppenheim's Signals & Systems, and I got really confused about it. I am trying to understand how I can show that a ...
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### Precursor ISI - causality violation?

Today, in my lecture on intersymbol interference (ISI), there was a discussion on postcursor ISI, and precursor ISI. Postcursor ISI is caused by the past bits, whereas, precursor ISI is caused by the ...
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### Does "improper" imply that a system cannot be stable and causal?

This answer and the comments in it made me wonder whether the following statement is true: If a transfer function is improper, then that system cannot be causal and stable at the same time. I had ...
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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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### Time-invariance, causality and stability of $h(t)$ of four given systems

Question: The impulse response functions of four linear systems $S_1,\ S_2,\ S_3,\ S_4$ are given respectively by \begin{align} h_1(t)&=1\\ h_2(t)&=u(t)\\ h_3(t)&=\frac{u(t)}{(t+1)}...
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### Why is $y(t)=x(t/2)$ a non-causal system?

I was going through my signal and system notes.they say $y(t)=x(t/2)$ is a non causal system? As non causal system depend on future inputs. how $t=t/2$ is future value of time? i could not understand ...
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### For a system to be causal, number of finite zeros <= number of finite poles. Why?

I read in this pdf that for a system to be causal, the number of finite zeros must be no greater than number of finite poles. Why? I know that for a system to be causal, $h[n]=0$ for all $n<0$. ...
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### Why can't a causal digital filter have an infinitely sharp transition between the passband and the stopband?

In DSP book by Proakis and as well as in this pdf, it is mentioned that practical causal digital filters cannot have an infinitely sharp transition from Pass-band to Stop-band. Why is it so? Can you ...
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### causality of the system $y[n] = x(2n)$

Can somebody please tell me why the system $y[n] = x(2n)$ is non-causal ? I know that causal systems depend on the past and present values of input and this system satisfies the condition. So why is ...
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### whether the system is linear or not for the given problem

Given the system: $$y(t)=x(t+1)+x(t−1)$$ is the system linear? For a system to be a linear first it should satisfy zero input and zero output. How can we calculate output at 0 input if the system ...
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### can $\frac{1}{H(z)}$ be causal and stable? [duplicate]

if we have linear phase FIR filter $H(z)$ which is causal and stable can $\frac{1}{H(z)}$ be causal and stable ? can it be causal without been stable ?
1 vote
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### Linearity, Causality and Stability of a System

Consider a system: $$y[n] = y[n-1] + u[n],$$ where $y[n]$ is the output and $u[n]$ is the unit step function. Is this system causal, linear, time-invariant and stable ? My attempt at the ...
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### Proof of Paley-Wiener criterion for causality

The Paley-Wiener criterion for causality is that $\displaystyle\int_{\mathbb{R}}\frac{A(\omega)}{1 + \omega^2}\mathrm{d}\omega$ exists and is finite, where $A(\omega) = \left|\mathcal{F}[f]\right|$ is ...
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### How to analyse anti-causal discrete transfer function using matlab?

Consider a discrete transfer function that represents an anti causal filter such as a derivative filter: $$H(z) = (-z^{-2} -2z^{-1} +2z +z^2) (1/8T)$$ Where T is the sampling period. Normally in ...
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### Definition of minimum-phase system

I saw a couple of definitions for minimum-phase in different textbooks and I'm trying to understand what the implication of each of them. The first definition I saw was: An invertible system which ...
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### Two real time signals convolving

This might be a stupid question but is it possible to convolve two real-time signals together? I know that generally for running convolution you have the IR and the block of the real time signal and ...
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### Causality and ROC of a stable LTI system

So I am looking at a stable LTI system whose input is $x[n]$ and output is $y[n]$. The equation relating the two is here: $$y[n-1]-\frac{10}{3}y[n]+y[n+1]=x[n]$$ I was able to compute its system ...