# Tag Info

## Hot answers tagged random-process

16 votes
Accepted

### What are the statistics of the discrete Fourier transform of white Gaussian noise?

Math tools We can do the calculation using some basic elements of probability theory and Fourier analysis. There are three elements (we denote the probability density of a random variable $X$ at ...
• 1,006
16 votes
Accepted

### What is a good example of an ergodic process?

Just suppose I give you a series of numbers, and I tell you they were picked randomly. And you know I am not trying to deceive you. Numbers are: $3$, $1$, $4$, $1$, $5$, $3$, $2$, $3$, $4$, $3$. I ...
• 30.6k
14 votes

### What is a good example of an ergodic process?

From the wikipedia article: a stochastic process is said to be ergodic if its statistical properties can be deduced from a single, sufficiently long, random sample of the process. In other words: ...
• 26.9k
11 votes
Accepted

### Why is $A\cos(2\pi f_ct)$ a non-stationary process?

A random process is a collection of random variables, one random variable for each time instant. It is best to write the random process as $$\{X(t)\colon -\infty < t < \infty\} \tag{1}$$ where ...
• 19.1k
10 votes
Accepted

### Understanding of Random Process, Random Variable and Probability Density Function

when we observe the Random Process at a specific time $t_k$, that is the value at $X(s_1,t_k), X(s_2,t_k),\ldots,X(s_n,t_k)$, if we denote them by $(a_1,a_2,\ldots, a_n)$. Now the mapping between ...
• 5,865
10 votes

### How can a signal be both periodic and random?

Most realistic signals are both random and periodic. For example, you can modulate a harmonic oscillator with a slow enough random signal that moves its frequency around a $\mu_{f}, \sigma_f$. This ...
• 10.2k
8 votes

### If the mean of a random process is constant, does it imply the process is first order stationary?

In the usual sense of the term, first-order stationarity means that the first-order distribution of all the random variables is the same: each $X_t$ has the same CDF, and so the same pdf (or pmf) too ...
• 19.1k
8 votes

### Gaussian White Noise - Relation Between Distribution and Correlation

When we say the stochastic process $X_{t_1}X_{t_2}\cdots X_{t_i}$ is a Gaussian Process with mean $\mu$ and variance $\sigma^2$ it only means $$X_{t_i}\sim\mathcal{N}(\mu,\sigma^2)$$ So still we know ...
• 4,135
8 votes
Accepted

• 19.1k
4 votes

### Why is $A\cos(2\pi f_ct)$ a non-stationary process?

In easy words: A process is stationary if its stochastic properties are independent of the time you look at it. Think of it like this: A stochastic process is just a Random Variable (RV) that, ...
• 26.9k
4 votes

### Interpretation of Histogram in Statistical Image Processing

Does it assume that each pixel in images obey the same probability distribution for the histograms of images? Images of different scenes will definitely not obey the same probability distribution of ...
• 23.1k

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