Questions tagged [random-process]

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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 ...
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1answer
1k 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 $f_0$, $A$ ...
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1answer
70 views

Power spectrum of uniform white noise

Given a white noise image $W_{i,j} \sim U[a,b]$ where each pixel is distributed uniformly in $[a,b]$, how would I go about computing its power spectral density? That is, I want to find $E[|\hat{W}_{i,...
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1answer
46 views

How to create a wide-sense stationary time series with a frequency of 40 Hz?

I want to create a time series in MATLAB which has a peak frequency of 40 Hz but is also a wide-sense stationary random process. I then want to use power spectral density estimation to recover the ...
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0answers
44 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 ...
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0answers
18 views

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 ...
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1answer
81 views

Questions about the stability (and stationarity) of a system and state space representations

i'm pretty new to the topic and I'm trying to understand how to determine the stability of a process. I'm giving this discrete-time stochastic system: $$ \cases{ s_t = 2s_{t-2} + 3w_{t-2} \\ y_t = ...
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1answer
89 views

An Interesting Model with Unknown Orthogonal Design Matrix

Suppose the multivariate one-way anova model for the raw data , i.e. $$ \label{Example_model_1} \mathbf{y}_{ij}=\mathbf{\mu}+\mathbf{z}_i+\mathbf{e}_{ij}, ~~ i=1,\ldots,m,~~j=1,\ldots,n_i,~~~~~~~~~~...
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0answers
35 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 ...
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252 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)...
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28 views

How to measure Noise

If I have a model that determines the current flowing through a membrane - how can I find out how big the random fluctuations in the current are? so how big is the noise level?
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37 views

Understanding white Gaussian noise variance

Referring to the bellow figure, assume the WGN has a constant PSD equal to N0. When filtered at $B_1 = 100 Hz$, the variance of the time domain noise is $σ_1^2$, and when filtered at $B_2 = 5 Hz$, the ...
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1answer
143 views

Blind Estimation of Signal Parameter and Noise Variance

Let $y[n]= h*x[n] + w[n]$, where $h$ is an unknown but deterministic parameter, $x[n]$ is a BPSK random variable with equal probability of +1 and -1, $w[n]$ are i.i.d. Gaussian with zero mean and ...
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22 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 ...
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6 views

Clutter Model in MOT: joint distribution of a random matrix and its column size variable

Suppose $C_k$ is a random matrix contains columns of measurement vectors that are random variables: $$C_k=[c_k^1,...,c_k^{m_k^c}]$$ $m^c_k$ is the number of columns as well as a random variable. All ...
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2answers
115 views

Why is there only one integration in the solution if there is two integral in the formula?

In this problem the random variable is theta and according to the formula there should be two integrations but in the solution there is only one . Nor am i able to understand the meaning of x1 and x2 ...
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61 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, ...
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28 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?
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18 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 = \...
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1answer
46 views

Particular 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 ?
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1answer
136 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[...
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38 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 ...