# Questions tagged [causality]

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79 views

### 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 ...
733 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 ...
646 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 ...
105 views

### 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 ...
57 views

### 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 ...
83 views

### 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 ...
55 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, ...
1 vote
35 views

### 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 ...
1 vote
165 views

### 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 ...
81 views

### 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 ...
1 vote
120 views

### 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 ...
358 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 ...
40 views

### 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 ...
35 views

### Causal LTI System LCCDE function in python

Can any write a code for this? Struggling to get it using np.sum() and np.roll() code snippet
115 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 $H(z)$?
219 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 ...
1 vote
122 views

### 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 ...
560 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 ...
114 views

### Sufficient conditions for invertibility of discrete LTI systems [duplicate]

Is $h \neq 0$ 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 ...
136 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 ...
480 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 ...
1 vote
128 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 ...
278 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 ...
1 vote
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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 ...