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
581 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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26 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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223 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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34 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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19 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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24 views

Low pass representation of Bandpass Random process

Can A WSS random process with non-zero mean be also represented in such form.
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34 views

How to Derive Rayleigh distribution using transformation formula

Consider a complex random variable $Z=X+\jmath Y$, where the probability density function of $X$ and $Y$ are given by $$p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} {\rm e}^{-\frac{x^2}{2\sigma^2}}\quad\mbox{...
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17 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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56 views

Analytical spectral density of a On/Off modulation defined by a Bernoulli process

Consider a narrow band signal (laser) that I can modulate digitally with a on/off switch controlled by a digital pseudo random number generator. The resulting signal features a linewidth broadened by ...
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22 views

Images as Markov chains

I have seen literature on representing black and white images as probability distributions and then computing "distances" between them, for example, in optimal transport. I was wondering if there is ...
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59 views

On the spectral representation of deterministic and random signals

I went back to many references in order to fix some of the confusions that I have on many concepts in signal spectral representation. I concluded that: 1) Deterministic signals may be represented ...
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14 views

Rate distortion function for a Gaussian process with a squared exponential kernel

This is probably a question whose answer should be available in some paper or textbook, but my searching for it hasn't helped me find a result that I could use. The question is basically just what ...
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1answer
29 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
123 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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36 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 ...