Questions tagged [random-process]
A random process (in time), also called "stochastic process" is a signal that, when sampled at any given time, is a random variable.
39
questions with no upvoted or accepted answers
3
votes
2
answers
314
views
Power Spectrum Density and Frequency
if i have some random signals (sampling rate = 10Hz, 0.1s per data)
Using python library i transformed it to power spectral density
power spectral density forms = f, psd (using mlab.psd)
I'm really ...
3
votes
0
answers
150
views
Energy Detection in Presence of Colored Gaussian Noise
Before asking my question, let me introduce the context:
For spectrum sensing based on energy detection, which has been widely studied in presence of AWGN, the optimal detection threshold is computed ...
3
votes
1
answer
3k
views
Calculation of an autocorrelation function
A sample of a random process is given as:
$$
x(t) = A\cos(2\pi f_0t) + Bw(t)
$$
where $w(t)$ is a white noise process with $0$ mean and a power spectral density of $\frac{N_0}{2}$, and $f_0$, $A$ ...
2
votes
0
answers
134
views
Random telegraphic noise and Lorentzian noise power spectral density
Following the example of the Lorentzian noise power spectral density shown above (ref), I would like to clarify the following:
In the first figure (labeled by (c)), May I please know why the constant ...
2
votes
0
answers
15
views
Condition for these sequences to be stationary correlated (tipp for integration of exponential functions)
I have two sequences $s$ and $r$ defined as :
$s = \{s_n\}_{n \in \mathbb{Z}}$ where $s_n(t) = (M_{\beta}^n s)(t) = s(t) e^{int}$ with arbitrary $s \in L^2(\mathbb{R})$ and $\beta > 0$
$r = \{r_n\}...
2
votes
0
answers
35
views
Signifance of statistical information in a signal
I am learning control engineering for some time and I work with a lot of transfer functions and frequency domain design. Reading from textbook, to me everything seems deterministic. Whenever I come ...
2
votes
1
answer
62
views
Estimate Local Noise Intensity in an Image
Noise can be assessed in uniform regions of an image, by subtracting a lowpass-filtered version of it. Then from the histogram of intensities, a global measure can be obtained (such as the average ...
1
vote
0
answers
28
views
Weiner Filter - why does this computation explain that the necessary filter is a weiner filter?
$X_1(t), X_2(t)$ are random WSS processes with expectation 0, and correlation functions $R_{X_1}(\tau), R_{X_2}(\tau), R_{X_1,X_2}(\tau)$ $n(t)$ is a white noise with SPD $S_n(f) = \frac{N_0}{2}$ ...
1
vote
0
answers
74
views
random signals through LTI systems, why are these two signals joint wide sense stationary?
I’m trying to solve this problem but I don’t understand an assumption the solution makes:
The question:
let $\hat{W}$ be the best linear approximation of $W_t$ out of $Y_t$, find $\text{CoV}(W_4, \...
1
vote
0
answers
56
views
Incorrect Power Calculation in MATLAB Convolution
I have been working on a MATLAB code to perform convolution and calculate the power of the resulting signal. However, I have encountered an issue with the power calculation in my code.
I am convolving ...
1
vote
1
answer
174
views
Does bandlimited power spectral density correspond to original WSS random process being bandlimited almost surely?
If it is given that PSD of a random process is bandlimited to frequency $f_B$, then can we claim that any sample path of the random process is also bandlimited to $f_B$?
Intuitively, I always thought ...
1
vote
0
answers
183
views
Power Spectral Density and Wiener–Khinchin theorem for 2 different stochastic processes
I know the famous Wiener-Khinchin theorem for stationary random processes: the Fourier transform of the autocorrelation function of a stationary random process is equal to the Power Spectral Density ...
1
vote
0
answers
117
views
Limiting value of autocorrelation of wide-sense stationary process
Let random process $X$ is wide-sense stationary process. Where could I find the source or verification of the statement that, when the limiting value of autocorrelation $\lim_{\tau\rightarrow\infty}...
1
vote
0
answers
78
views
Response of an unstable LTI system to random signals
A convenient approach for studying the response of a stable LTI system with impulse response $h(t)$ to a WSS stochastic input $X(t)$ is to look at the power spectral density (PSD) of the output $Y(t)$ ...
1
vote
0
answers
205
views
Randomly Generate Synthetic Noise in an Image Text Document
I'm working on denoising dirty image document. I want to create a dataset wherein synthetic noise will be added to simulate real-world, messy artifacts. Simulated dirt may include coffee stains, faded ...
1
vote
0
answers
90
views
Relation between power spectral density and mean absolute value
The root mean square
$$\sigma_{x} = \sqrt{\frac{1}{T}\int_0^T x^2(t) \, \mathrm{d}t}$$
of a finite zero-mean random signal $x(t)$ in the range $0 < t < T$
is related to the signal's power ...
1
vote
0
answers
286
views
Gauss Markov Process
I am trying to generate a random signal that represents a gyroscope drift. I know the Allan Variance characteristics of the signal (ARW, RRW, Bias Instability and Cluster Time for for Bias Instability)...
0
votes
0
answers
37
views
Related to SNR in wireless communication
I am working on a research paper related to wireless communication, wherein I am facing some doubt while writing expression of SNR (which is a ratio of Signal variance in numerator to Noise variance ...
0
votes
0
answers
22
views
Understanding Fresnel reflection coefficient formula
In textbook "Wireless Communications Principles and Practice" by Theodore S. Rappaport, the expression of Fresnel reflection coefficient ($\Gamma$) for parallel polarization is given as
$\...
0
votes
1
answer
38
views
Why different noise terms are read at specific sampling interval in Allan Variance plot?
I was trying to identify Quantization Noise, Angle Random Walk, Bias Instability, and Rate Random Walk from Allan Variance plot which as Allan deviation on y axis and Sampling Time Interval ...
0
votes
0
answers
44
views
Struggling with visualizing (drawing) a sample of a random process
I've had this question I don't really know how to answer.
let $t \ge 0$, $N_t$ is a possionian random process with parameter 1. let $-\infty < t < \infty$, $X_t$ is a random process that is ...
0
votes
0
answers
63
views
What is the difference between the general white process and the white process of order 𝑝?
Antoni uses the following definition of white process of order $p$:
a process whose all cumulants up to order p are such that
$$\text{Cum}\left[X(t),X(t-\tau_1)\cdots,X(t-\tau_{r-1})\right]=C_{rX}\...
0
votes
0
answers
19
views
Is this signal an FRI (finite rate of innovation) signal?
I am trying to model the subsurface as a randomly layered medium, with stochastic acoustic attentuation that gives rise to a reflected waveform from an active source as the following signal:
$$
x(t) = ...
0
votes
0
answers
68
views
Symmetric Autocorrelation Function vs Asymmetric Autocorrelation Function
I am trying to work through the Cyclostationary Blog to create a cyclic autocorrelation function:
I have been given the above equation to determine the cyclic autocorrelation function where tau is ...
0
votes
0
answers
30
views
The frequency function for $Y_t-18=0.4X_t+0.9X_{t-1}+e_t$
I am having trouble finding the frequency function that takes me from $X_t$ to $Y_t$ in the system stated in the title. $X_t$ and $Y_t$ are stationary stochastic processes and $e_t$ is zero mean white ...
0
votes
0
answers
144
views
What is the difference between Yule Walker and Modified Yule Walker Equation that used in Stochastic Signal Modeling?
Our Professor couldn't explain the clear difference between the Yule Walker equation and the Modified version of it that is used in Stochastic models. Please explain both the equations and why we ...
0
votes
0
answers
19
views
Probability of the rate of change of a filtered random process
I am given the following problem: I have a filter with impulse response $h(t) = e^{-10t}, t \leq 0$, and autocorrelation function of the input signal, which is WDS and Gaussian with median equal to 0, ...
0
votes
0
answers
290
views
The definition of amplitude probability density
I'm trying to figure out the formal definition of "amplitude probability density"(APD). First of all I didn't find a textbook which defines APD but there are some sources that explain it ...
0
votes
0
answers
40
views
Global variability index for group of signals
Suppose I have a method that I can use to generate $n_p$ signals (we can intend them as realizations of an unknown not stationary discrete-time stochastic process). Modifying the method, I can obtain ...
0
votes
0
answers
214
views
Signal-to-Noise ratio of multivariate stochastic process from Correlation Matrix
I'm not in signal processing, I'm from an another discipline. I've derived a simple result which I presume must be well known in SP and I'd like to know whether there's a paper or textbook that has it ...
0
votes
0
answers
56
views
How to characterize the randomness of an event using it's PSD?
I have the power spectral density function of a stochastic phenomenon.
how can I generate a signal (time series) representing the randomness of this event over time?
How can I draw the probability ...
0
votes
0
answers
35
views
How to compute the energy of a NON-STATIONARY (transient) random discrete-time signal
When computing the energy of a NON-STATIONARY (transient) random discrete-time signal $x(n)$, does it make more sense to compute the energy as
$ E=\sum_1^N{x^2(n)}$ over all the $N$ samples
or does ...
0
votes
0
answers
121
views
Proof of weak stationary random process autocovariance always goes to zero?
Professor told me that if a random process is weak stationary, and it does not feature any periodic component, then its autocovariance always goes to zero.
I can intuitively understand it, however, ...
0
votes
0
answers
114
views
Is the expectation of a random process $X(t)$ with zero DC component necessarily zero?
Is the expectation of a random process $X(t)$ with zero DC component necessarily zero? Or can it be non-zero depending upon the process?
0
votes
0
answers
21
views
Early estimate the sign of the drift in a generalized Wiener process
I posting here my problem, perhaps somebody can point me how to proceed further :)
[The challenge]
I have an electronic system that can be modeled as a Wiener process with a drift $\mu$:
$ X_t = \...
0
votes
0
answers
44
views
How to determine if output signals represent the same process with different unknown random inputs
This is a question about how to determine if two different output signals represent the same process with different random inputs. This is related to validating ship motion modeling. When ship motion ...
-1
votes
1
answer
117
views
Random Signal Energy
Why the energy of random signal(random process) is infinite? and why random signal can not be zero at infinity?
I know that there is a relation between the tow questions but I'am still confused.
-1
votes
1
answer
153
views
Kalman Filter's Correlation Formula
I'm reading a book where the autocorrelation of white noise is expressed as:
What is the term $Q(k)$ and why is is expressed as an average value of a dot product ?
-1
votes
1
answer
176
views
Approximating a Gaussian Process
Suppose that $\theta_t$ is an exogenous variable with known Gaussian process. Next, suppose that for any index $i\in [0,1]$,
$$ a_{i,t} = (1-\beta)\mathbb E[\theta_t|\mathcal I_{i,t}]+\beta \mathbb E[...