Questions tagged [stochastic]
The stochastic tag has no usage guidance.
79
questions
0
votes
1answer
249 views
PDF of a Shifted Rectangular Pulse
I wanted to determine the PDF of a Stochastic Process. I am familiar with the concept of PDF for a Random Variable which maps the outcomes to its probabilities but I am not able to find the PDF of a ...
3
votes
1answer
790 views
Average Power Spectral Density of PAM signals
I am reading through the PAM transmission scheme and about the power spectral density of the signals. Given that the Average Power Spectral Density of PAM Signals is:
$$
\Phi_{ss}(f)=\Phi_{aa}\left(e^...
1
vote
1answer
1k views
Autocorrelation and Power Spectral Density (Discrete)
The Autocorrelation, $\phi_{aa}[\kappa]$, of a discrete time random process, $a[k]$, is defined as:
$$ \phi_{aa}[\kappa] = \mathrm{E}\left\{ a[k+\kappa]a^*[k] \right\} $$
Taking its fourier ...
0
votes
2answers
78 views
Stochastic approximation algorithm
The goal is to find the FIR filter coefficients $\mathbf{h} = [5;3]$ with the help of the adaptive FIR filter $\mathbf{w}$ of order $p = 2$.
I have implemented the Stochastic approximation algorithm ...
1
vote
2answers
1k views
Understanding the definition of mean/autocorrelation
I was studying about the definitions of mean, expected value and autocorrelation. I wanted to verify my understanding the evaluation of mean, expected value and autocorrelation. At the same time to ...
1
vote
1answer
191 views
Understanding of Random Process/Random Variable
At a simpler level to my previous question, I wanted to confirm my understanding on Random Process based on Random Variables using an example.
So, I took this example:
If we consider a dice, which ...
5
votes
1answer
3k views
Understanding of Random Process, Random Variable and Probability Density Function
I just wanted to confirm my understanding of a Random Process, Random Variable and the its Probability density Function.
Here is the way that I looked a Random Process/Random Variable:
If we ...
0
votes
3answers
306 views
What really means stochastic in field of signal processing
I met two definitions of word stochastic, the first one (cited from wikipedia Stochastic)
The word stochastic is an adjective in English that describes
something that was randomly determined
The ...
0
votes
1answer
227 views
LTI filtering for wide-sense stationary process
Why is it that if $U[n]$ is wide-sense stationary and it is convolved with $h[n]$ to produce $W[n]$, the autocorrelation becomes $R_{WW}[n] = R_{UU}[n]*h[n]*h[-n]$?
I know that in general $R_{WW}[n_{...
0
votes
1answer
520 views
How to treat noise (in the acceleration) in a Kalman filter when tracking position?
I have an equation of motion for which I am wanting to track the position.
The equation looks like this:
$$\ddot{x}(t) = -a\dot{x}(t) - bx(t) + F(t)$$
where $F(t)$ is an external Stochastic force ...
6
votes
2answers
620 views
Why is $A\cos(2\pi f_ct)$ a non-stationary process?
I am studying analog communication and having Communication system - Simon Hykin as one of the reference.
There is a question
Consider the sinusoidal process$$X(t) = A\cos(2\pi f_ct)$$where the ...
3
votes
2answers
2k views
What's the meaning of ergodicity? [duplicate]
I just read the topic about Ergodicity but I have ambiguity about its meaning (by intuition). What does mean: (for mean) Statistical average = Time average. Could you please explain it in detail. ...
-1
votes
1answer
157 views
Analyzing fluctuations within the Signal
I am trying to figure out how to analyze the signal shown below. It shows the fluctuation of number of review in for a product in Amazon, where positive means addition number of review while negative ...
2
votes
2answers
504 views
What does the frequency axis of a Power Spectral Density mean?
I have never really understood what the frequency axis meant when we plot the Power Spectral Density(PSD).
Does it correspond to frequency as we get after we take the Fourier Transform of a time ...
5
votes
1answer
78 views
Is there any computational method to prove whether a series is stationary or not?
I have a discrete series $x[n]$. It is extracted from real life and I do not have probability distribution of each value $x[n]$. Is there any computational method to prove whether the series is ...
1
vote
1answer
182 views
Output of lowpass filter with damped sine wave input
The random process $$Y(t)=\cos(\omega_0t)\cos(\omega_0t+\pi N(t))$$where $N(t)$ is a Poisson process of parameter $\lambda$ enters a lowpass filter with transfer function $$H(j\omega) =
\left\{
\...
3
votes
2answers
140 views
If noise is your signal, what is your noise?
Consider the following contrived situation. Imagine a Gaussian white noise process $x[t]$, with bandwidth $Īf$, with PSD equal to some quantity $A$ which you would like to measure.
So the way to ...
1
vote
2answers
14k views
generating white gaussian noise in matlab using two different functions
I want to know the difference between the two Gaussian noises generated below? Which one is white and how can i make the other one white?
y=wgn(1,10000,0)
and
<...
0
votes
1answer
212 views
Ergodicity of joint process
If we have two processes and both of them are ergodic. Does this mean that the joint proces is ergodic? Or other way around? If we have the dynamics for both components of the joint process what are ...
3
votes
1answer
396 views
explanation of correlation of stationary stochastic processes
I have some doubts about correlation in stationary stochastic processes.
I know that the expectation of a random variable is
$$E(x)=\int_{-\infty}^{+\infty} a f_x(...
3
votes
1answer
3k views
Deterministic / Non-deterministic Stochastic Process
Problem 6.1-6 of Probability, Random Variables, and Random Signal Principles, 4th Edition by Peebles asks
If a process is defined by $X(t) = A$, where $A$ is a continuous random variable uniformly ...
0
votes
1answer
325 views
AR model order selection for half second EEG fragments
I am using MATLAB to evaluate power spectral density estimates of half second EEG signals, using modified covariance method. Can anyone suggest me how to select the AR model order for this process? Is ...
1
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0answers
1k views
Fourier transforms of random processes
In the Wikipedia article on Brownian noise, the Fourier transform of Brownian noise is determined. How is that Fourier transform defined? It seems it is a non-random quantity there, so it is not ...
0
votes
1answer
151 views
How to represent multiple related signals via mathematical function?
I have three data sets from same source. I know they are interdependent and stochastic also. The datasets are of very high frequency (see the graph, X axis is time and Y axis is value). I want to ...
0
votes
1answer
428 views
Is ergodic in mean a property defined only for WSS stochastic processes?
I understand the definition of a random process $X(t)$ being ergodic in mean (first-order ergodic) is that the expectation of the sample mean $<u_X>_T=\frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}...
0
votes
1answer
141 views
Properties of Stochastic Processes [closed]
I have a basic question about stochastic processes:
When some informations such as wss, uncorraleted sampled, white about random signal (say x[n]) are given, what do we exactly have?
For example ...
0
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0answers
3k views
Generate time-domain random signal from PSD
Given an analytical description of the PSD, for example (MATLAB "pseudocode"):
...
0
votes
1answer
115 views
How do we compute distrubtions of the value of a random process conditional on initial conditions?
Suppose I have a stationary process $\phi(t)$ with a known autocorrelation function
$$ A(\tau) \equiv \langle \phi(0) \phi(\tau) \rangle$$
and suppose I also know that $\phi(t)$ is Gaussian ...
4
votes
1answer
3k views
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 ...
