Questions tagged [random-process]
160 questions
28
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3 answers
Variance of White Gaussian Noise
It could seem an easy question and without any doubts it is but I'm trying to calculate the variance of white Gaussian noise without any result.
The power spectral density (PSD) of additive white Gaussian noise (AWGN) is $\frac{N_0}{2}$ while the…
Mazzy
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What is a good example of an ergodic process?
I'm trying to find simple examples of an ergodic process. What process comes to your mind as a good illustration of its properties?
A quick research (Wikipedia, another answer) mainly gives examples of non-ergodic processes. Also, I'm wondering…
bluenote10
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12
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What are the statistics of the discrete Fourier transform of white Gaussian noise?
Consider a white Gaussian noise signal $ x \left( t \right) $.
If we sample this signal and compute the discrete Fourier transform, what are the statistics of the resulting Fourier amplitudes?
DanielSank
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8
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Gaussian White Noise - Relation Between Distribution and Correlation
Im a beginner in signal processing so my question may be obvious.
A white noise has the property to have its autocorrelation function that is equal to
$$\mathbb{E}[f(t+\tau)f(t)]=\sigma^2 \delta(\tau).$$
We say that random signals can be Gaussian…
StarBucK
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7
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3 answers
Random signals as power signals
Why are random signals considered as power signals (i.e. signals with infinite energy and finite average power)?
Does this make any sense? What does it mean for random signals to have infinite energy even though we know that real-life signals…
Likely
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7
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Understanding Ergodicity and Ensemble Averaging
Literature says that a stationary signal is ergodic, if its ensemble average = time averages. Should it be the statistics computed by time averaging = statistics computed by ensemble averaging?The way I understood from the book in the link is as…
Srishti M
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6
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3 answers
How can a signal be both periodic and random?
Do any examples of such signals exist where the signal is both periodic and random? Because as I see it, if a signal is periodic then the randomness kinda goes away because you know what the signal will look like after some time.
dydx
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6
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Why is $A\cos(2\pi f_ct)$ a non-stationary process?
I am studying analog communication and having Communication system - Simon Hykin as one of the reference.
There is a question
Consider the sinusoidal process$$X(t) = A\cos(2\pi f_ct)$$where the frequency $f_c$ is constant and amplitude $A$ is…
TIWARI
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6
votes
1 answer
Variance of an Implicit Function of Kalman State Vector
Given a state vector, $ x $, given by $ x = {[r, v, a]}^{T} $ (Range, Velocity, Acceleration) the Time to Hit is the the time which holds the following:
$$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} = 0 $$
Now, given the State Vector covariance $ P…
Royi
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5
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2 answers
Understanding PSD: Why Does Power at High Frequencies Affect Low Frequencies?
I'm trying to wrap my head around power spectral density on a conceptual level, but I am having some difficulty. Suppose I have a communication system where I am receiving and sampling white Gaussian noise, which has a uniform PSD. Increasing the…
Probably
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5
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Understanding of Random Process, Random Variable and Probability Density Function
I just wanted to confirm my understanding of a Random Process, Random Variable and the its Probability density Function.
Here is the way that I looked a Random Process/Random Variable:
If we consider a sample space $S$ consisting of $n$ outcomes…
sundar
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5
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3 answers
Sum of Sine and Cosine with Random Phase as LTI System
I have the following system:
Where $ {H}_{1} \left( f \right) = {H}_{2} \left( f \right) $ and $ \theta \sim U[0, 2\pi]$ independent of any other factor in the system.
Given the input is identical, Is an LTI system?
Could you prove it?
Otherwise I…
Royi
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4
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3 answers
Under what conditions is there a one-to-one mapping between continuous-time and discrete-time signals?
As the sampling theorem dictates that the uniform sampling frequency must be at least twice the maximum frequency present in the bandlimited signal (Nyquist rate), a question arises about the uniqueness of this representation of the analog signal to…
HYMD
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4
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2 answers
Moving from deterministic signals to stochastic signals in s-domain (Power Spectral Density)
Assume we have the following system (coming from control systems theory, hence in s-domain)
$ Y(s) = H_A (s) \cdot A(s) - H_B (s) \cdot B(s) $
I now wish to consider $a(t)$ and $b(t)$ as white noise of unit variance, and I'm interested in the Power…
user53750
4
votes
1 answer
Conceptual Questions on Colored Noise Process
I am having a tough time finding answers to some specific questions and finding references where there is information regarding Brownian noise or Red Noise. I'm referring to white and colored noises where white noise can be Gaussian or Uniform Noise…
Sm1
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