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# Questions tagged [probability-distribution-function]

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49 views

### Regarding SINR (Signal to Interference Plus Noise Ratio) in wireless communication

I am working on a research paper related to wireless communication, wherein I am facing some doubt while writing expression of SINR (which is a ratio of Signal variance in numerator to Interference ...
1 vote
74 views

### Deriving the posterior distribution parameters of a normal distribution in the context of dereverberation

Context: $\bar{\Theta}$ is the room regression filter coefficients (RRC); $$X_{t} = \bar{\Theta}^{H}\bar{X}_{t-1} + s_{t}$$ means in words: the filter that defines how the room causes reverberation to ...
49 views

### Complex Gaussian distribution in snapshot model

In Chapter 5 of the Optimum Array Processing by Harry van Trees [1], the formula of the complex Gaussian distribution appears very different from the formula that is used elsewhere in the same book ...
1 vote
151 views

### Which probability density functions to use in a likelihood ratio test for the radar detection problem?

I am trying to understand the radar detection problem in the form of the generalized likelihood ratio test and am having a little trouble with understanding the noise distributions. Perhaps this will ...
• 15
1 vote
75 views

### How can I write the likelihood of this system

I am very confused about how to write the likelihood of the following function. I have tried one and it doesn't have a maximum at the point where it should contain a maximum. The formulation of the ...
• 107
1 vote
122 views

### Why is a random process strictly stationary when its joint Probability density function is time invariant?

I don't understand what stationarity of random process mean. I know they're statistical properties that are time invariant but I don't have intuition for it and I don't get what that has to do with ...
1 vote
61 views

### Understanding Quantile-Quantile Plot of my Signal

I have computed the Q-Q plot of my dataset, which is a recording from a brain signal, and it shows a curious left and right skewness displacement, and I was wondering if this is any other distribution ...
• 153
1 vote
57 views

### Help on choosing compatibility test for classification algoritm

I have designed an algorithm for classification and I need to add a suitability or compatibility test for accepting a signal as an input. Basically, not all signals are suitable for processing by my ...
• 153
124 views

### What is the sum $\sum_{m} e^{i (U_m k + \beta_m)}$ when $U$ and $\beta$ follow different distributions

I have the following function. $$x(k) = \sum_{m} e^{i (U_m k + \beta_m)}$$ $i = \sqrt{-1}$ Here, $U_m$ are samples drawn from a Gaussian random distribution. $$U_m \sim \mathcal{N}(\mu, \sigma)$$ ...
• 107
129 views

### How to transform bits of data (0 and 1) to uniform distribution

Question: I am looking for a way to transform a series of 1s and 0s to be distributed 50% 1s and 50% 0s. How do I do that? Background: I am a software engineer working on writing code for a ...
51 views

### Deriving the probability distribution function of the cross-spectral phase

I came across a research paper (\ref{Ref 1}) where the probability distribution of the phase of the cross-spectrum was derived. Unfortunately, I could not understand how the authors arrived at the ...
• 41
31 views

### n-dimentional integral over Multivariate Gaussian

given the prior distribution of $\mathbf{a}=[a_1,\ldots,a_K]^T$ as p_{\mathbf{a}}(\mathbf{a})= \frac{1}{\pi^K \det{\mathbf{R_{\mathbf{a}}}}} e^{\mathbf{a}^H \mathbf{R}_{\mathbf{a}}^{-...
• 135
91 views

### Calculate the probability of error of two vectors

I am trying to calculate the probability of error of two vectors, for example the first one is transmitting a modulated data $x$ with modulation order $M$ as following $y_1 = [x \ \ 0]^T$ while the ...
• 608
58 views

### (Dis-)connecting a stochastic signals spectrum from its pdf

How might one generate a sequence of N pseudo random numbers that simultaneously have an e.g. pink spectrum and are gaussian distributed? A hunch would be to first generate an uncorrelated white ...
• 3,434
41 views

### Adaptive Particle Filter: unknown process Equation

In my design and implementation of a SIR particle Filter, I don't have the state process equation of the actual system, which would have given a very good estimation of the real signal. I was ...
• 41
230 views

### Why the received SNR increases with bandwidth?

I am performing the following simulation: Complex chirp signal with bandwidth [-B, B] is transmitted through a multipath channel which has $N$ taps all being complex Gaussian variables (i.e., ...
192 views

### Is it possible to compute the PSD of s(t)^2 given the PSD of s(t)?

Given a well-behaved signal $s(t)$ given by, $s(t) = \sum_{i}^{N} \cos( \omega_it + \phi_i)$ with a large $N$ and a well-known power spectral density (PSD), $\tilde{S_1}(\omega)$. Is it possible to ...
• 183
1 vote
194 views

### How to generate a power-law / pink noise signal?

Suppose I need to generate a time series where the intervals will be about 120 seconds every time, but with a small variation (e.g. 125, 130, 119, 118, 121, 129, etc) I want this variation not to be ...
• 125
576 views

### simple explanation of rank transform and its relation to normal distribution

I tried to understand the rank transform, but I couldn't. The first step common to all histogram remapping techniques is the transformation of the pixel intensity values of the given image via the ...
• 349
297 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 ...
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88 views

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### Related to wireless channel fading

I am reading some papers wherein a wireless channel is assumed as zero mean circularly symmetric complex Gaussian (ZMCSCG) with unit variance and it is also mentioned that the channel undergoes ...
• 17
776 views

### Why the value of Gaussian curve drop to 1/19 at 2 standard deviation?

Taken from Guide to DSP where it says: ... at two ... standard deviations from the mean, the value of the Gaussian curve has dropped to about 1/19 ... It seems to be a straight forward calculation ...
• 207
72 views

### How to write a complex symmetric gaussian signal [closed]

In my work I need to use this signal of complex symmetric gaussian noise signal represented as $w$. But I don't know exactly how to represent it
102 views

### If two signals have different distributions that you know and can model, can you use that to separate them?

For example, if I have a mixed signal composed of signal A added to signal B, and I know that the histogram of signal A is non-Gaussian in the time domain, and that the histogram of signal B is ...
• 1
1 vote
204 views

### Expected Value of a sequence with two random variables

If I have a signal of the form $x\left(n\right)=Acos\left(nω+ϕ\right)$ where $\omega \in \left[\omega -\lambda ,\omega \:+\lambda \:\right]$ is a uniform random variable and $\phi$ is also a uniform ...
• 303
431 views

### How do you derive the new mean and variance when two gaussian functions are multiplied together?

I'm trying to understand the contents of this web-page which suggest that multiplying two Gaussian functions together produce a new Gaussian function with a new mean and variance. Say I have the two ...
• 872
1 vote
58 views

### Nonuniform sampling points based on the first order derivative of signal amplitude

Problem: I need to measure a experimental data set $y(x)$. However, the experiment is extremely time-consuming and I don't have the luxury to have linearly spaced sampling point $x$. I need the ...
• 121
125 views

### Multivariate Histogram / CDF Matching for Image Color Matching

Suppose X is random variable that is spatial position in finite range, which its Cumulative Distribution Function (CDF) could be calculated easily, then if I have two random variable X and Y spatial ...
258 views

### Sifting Property of Shifted Impulse

In the SE Chemistry forum, someone posted an interesting question on converting a scaled and shifted delta function into Lorentzian by convolution please see "simulating a molecular spectrum"...
• 569
2k views

1 vote