Questions tagged [random]
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75 questions
0 votes
2 answers
497 views
Limitations of C's rand function usage in DSP
I am using the rand() function in C to generate white noise in DSP processors, but its behavior varies depending on where it is called. I have posted a question on ...
- 21
0 votes
0 answers
65 views
Calculating return time in random proccess
how can we calculate the time that a random process $h(t)$ with mean $\mu$ and variance $\text{Var}_h$ to return to its mean ($\mu$) after being less than $\mu$ ?
- 11
0 votes
0 answers
56 views
Possible to combine and/or compare a swept Sine and a wide band noise signal?
I am working on a problem where two profiles need to be compared. One is a swept sine in $m/s^2$ (Acceleration) and the other is a sine-on-random signal composed of a swept sine $m/s^2$ and a random ...
0 votes
2 answers
284 views
How do random processes add in Rayleigh fading to get a Guassian random process?
I was studying Rayleigh channels from Wireless Communications, Second Edition by Andreas F. Molisch. The book states that by adding different in-phase and quadrature components multipath components ...
1 vote
0 answers
109 views
Properties of pseudorandom ternary sequences
For pseudo-random binary sequences, we know there are various properties: Autocorrelation, balance, Fibonacci vs Galois modes. These are all well-known. However, for pseudo-random ternary sequences, I ...
- 153
1 vote
1 answer
337 views
Autocorrelation of random walk
I want to analyze the auto-correlation of a received power signal that I captured. Unfortunately, I cannot publish the data but I found the same problem arises for a random walk, that's why I used the ...
- 13
0 votes
0 answers
50 views
Help with creating/drawing the PDF of signals X and Y
Given is an analogue source $x$ equally distributed in the interval $[-1;+2]$. By means of a mapping, the signal $Y$ is calculated according to $Y = (X - 1)^3$ is generated. Sketch the $PDF$ of the ...
- 1
0 votes
0 answers
73 views
Random projection with compressive sensing and hashing algorithms
I read that Random Projection matrices can be used in both Compressive Sensing and Locality Sensitive Hashing. I need simple explanation for the difference between applying Random Projection in both ...
- 33
0 votes
1 answer
786 views
Determining the average probability of error
I'm trying to solve the following problem: In a binary PAM system, the input to the detector is $$y_m = a_m+n_m+i_m$$ where $a_m = \pm1$ is the desired signal, $n_m$ is a zero-mean Gaussian random ...
- 680
0 votes
0 answers
71 views
What types of distributions (except the Gaussian) that follow for random jitter in a correlated signal?
For the simple case, let's consider the correlated signal $s$ with jitter (without noise) as follows: \begin{align} s(t, \theta_i) = \cos(2\pi f (t + \epsilon_t) + \phi + \theta_i), ~~ i=0,1, ... \end{...
- 3
0 votes
3 answers
1k views
If $X$ and $Y$ are zero mean independent Gaussian random variables with different variances, what is the density of $\sqrt{X^2+Y^2}$
Let $X\sim\mathcal{N}(0,\sigma_X^2)$ and $Y\sim\mathcal{N}(0,\sigma_Y^2)$ be independent Gaussian random variables. What will be PDF of $Z=\sqrt{X^2+Y^2}$ and $W=\arctan{\left(\frac{Y}{X}\right)}$. ...
- 351
0 votes
0 answers
30 views
Proving that this process is weakly-stationary [duplicate]
Let $X(t) = Acos(2\pi f_c t)$ be a random process where $A$ is a uniform random variable within $(-1,1)$. I'm trying to prove this is a weakly(i.e. wide sense) stationary process. I need to show two ...
- 101
1 vote
1 answer
92 views
Why the requirement of the GCD of the lengths of all circuits in the graph being one?
I am reading A Mathematical Theory of Communication. The second requirement of an ergodic process confuses me (emphasis mine): All the examples of artificial languages given above are ergodic. This ...
- 125
-1 votes
2 answers
162 views
Probability of error for detection problem
Let $X \in \mathbb{R}^N$ and $Z \sim \mathcal{N}(0, \sigma^2 I)$ be random vectors. $Y = X + Z$ $X$ can be either $a_0 \in \mathbb{R}^N$ or $a_1\in \mathbb{R}^N$ with equal probability. So the ...
- 119
-1 votes
1 answer
505 views
Coherent Radar -- How do we justify it?
How can we justify doing coherent radar when the phase of the return is unknown? For instance, after a reflection, assuming a stationary target, we should get something akin to: $$ x_{rx}(t) = |\...
- 129