Questions tagged [causality]

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3answers
259 views

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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1answer
58 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 $X[k]$ ...
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1answer
56 views

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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27 views

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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0answers
54 views

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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0answers
37 views

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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1answer
73 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 ...
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3answers
1k 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: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$...
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2answers
56 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 ...
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0answers
86 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 ...
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2answers
133 views

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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1answer
64 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 $y(0^-) = 2, \dot{y}(0^-) = 1$. $...
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0answers
38 views

Extrapolation of band-limited frequency data

I'm now studying "How to do accurate transform from band-limited frequency data specifically S-parameter data of high speed interconnect to the causal impulse response in time domain. There are ...
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19 views

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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1answer
67 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'....
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1answer
34 views

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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1answer
157 views

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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32 views

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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1answer
307 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. ...
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1answer
220 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) = \...
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1answer
100 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 ...
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1answer
33 views

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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2answers
226 views

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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3answers
42 views

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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2answers
183 views

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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1answer
205 views

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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1answer
38 views

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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1answer
451 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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2answers
116 views

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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1answer
253 views

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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1answer
177 views

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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4answers
657 views

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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1answer
128 views

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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3answers
191 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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1answer
150 views

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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1answer
112 views

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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3answers
2k views

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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1answer
200 views

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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4answers
4k views

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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0answers
53 views

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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2answers
2k views

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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0answers
321 views

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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1answer
447 views

Causal LTI system having exponential input

I know that for an LTI system having complex exponential input, i.e, $x(t)=\exp(j w_o t)$ & $h(t) \to $ LTI System ; then, its output { $y(t) \} =M \exp(j w_o t + \phi)$ , where $M= |H(j w)|_{|w= ...
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1answer
551 views

Why the frequency response plots (of causal filters) only show positive frequency?

Take an example of the below plot for an LPF (Source : WikiPedia) The plot starts from $0$. We know that the fourier transform of any signal brings in negative frequencies due to complex exponentials ...
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1answer
426 views

System that has derivative of input is non causal

Consider a system $y(t) = \dot{x}(t)$ where $y$ is the output and $x$ is the input. Given an initial condition $x_0$ and two inputs $x_1$ and $x_2$ such that $$x_1(t)=x_2(t) , 0 \le t < t_0$$ the ...
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1answer
33 views

Causality of the given system

I am given the following discrete system $$y[n]=x[-n]$$ where $$x[n]=n+3$$. Now from what I understand, since $$y[n]=x[-n]$$ therefor the system is causal as the output is depending on the ...
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1answer
118 views

Finding the transfer function of a discrete signal described by two equations

A discrete time system is described by the following system of equations. $$q[n] = \big(x[n]-\frac k4q[n-1]\big)$$ $$y[n] = \big(q[n]-\frac k3q[n-1]\big)$$ Find the systen function and then find the ...
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2answers
1k views

Realization of a filter based on its transfer function

How can we check whether the filter is realizable given its transfer function and What are the parameters the realization depends on? Here is an example: Show that a filter with transfer function $H(...
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2answers
2k views

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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1answer
1k views

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 ...