Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [causality]

81 questions
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What is the easiest, most straight-forward way to prove this about minimum-phase filters?

Using the "unitary" or "ordinary frequency" or "Hz" convention for the continuous Fourier Transform: $$ \begin{align} X(f) \triangleq \mathscr{F}\{x(t)\} &= \int\limits_{-\infty}^{\infty} x(t) \, e^{-j 2 \pi f t} \, dt \\ \\ x(t) =…
robert bristow-johnson
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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. In this example, 3 narrow band signals (high…
VMMF
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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)=\frac{dx(t)}{dt}=\lim_{\Delta t\to…
Nishanth Rao
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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 please provide a detailed explanation (with…
Nagabhushan S N
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Causal system and Physical Systems

According to the Paley-Wiener criterion, a system is causal if satisfies: $$\int\limits_{-\infty }^{+\infty }{\frac{\ln (|H(f)|)}{1+{{f}^{2}}}}df<\infty$$ So I want to know This equation is related to LTI system only? Only casual system is…
Ehsan Zakeri
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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 broader context of continuous-time linear…
Marca85
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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 thought that this was true for a while. But the…
Tendero
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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 $X[k]$ with $k \in [0...N-1]$ also has the property that…
Dan Boschen
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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: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$ Where $w[n]$ is the output of the leftmost…
uriyaba
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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 the modulus of the Fourier transform of a…
nimish
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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 then you convolve them both, making sure you have…
gabrielzalles
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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 that the derivative of the output is related to a…
SPARSE
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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 any applications of anticausal systems. So why…
Paddy
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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 how? could somebody please explain it to me?
uzair ahmad khan
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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 $n<0$. Can you give an explanation how the statement maps to…
Nagabhushan S N
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