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Questions tagged [probability-distribution-function]

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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 ...
Pranu's user avatar
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1 answer
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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 ...
user3371266's user avatar
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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 ...
Tommi Rimpiläinen's user avatar
1 vote
1 answer
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 ...
Jim's user avatar
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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 ...
CfourPiO's user avatar
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1 answer
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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 ...
mahmoud esmail's user avatar
1 vote
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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 ...
GGChe's user avatar
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1 answer
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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 ...
GGChe's user avatar
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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. $$ U_m \sim \mathcal{N}(\mu, \sigma) $$ ...
CfourPiO's user avatar
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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 ...
Eyal Gerber's user avatar
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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 ...
rill's user avatar
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n-dimentional integral over Multivariate Gaussian

given the prior distribution of $\mathbf{a}=[a_1,\ldots,a_K]^T$ as \begin{equation} p_{\mathbf{a}}(\mathbf{a})= \frac{1}{\pi^K \det{\mathbf{R_{\mathbf{a}}}}} e^{\mathbf{a}^H \mathbf{R}_{\mathbf{a}}^{-...
zahraesb's user avatar
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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 ...
Fatima_Ali's user avatar
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3 answers
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(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 ...
Knut Inge's user avatar
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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 ...
doumham's user avatar
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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., ...
Miroslav's user avatar
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1 answer
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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 ...
Gyromagnetic's user avatar
1 vote
1 answer
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 ...
Aerodynamika's user avatar
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1 answer
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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 ...
Noha's user avatar
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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 ...
S.H.W's user avatar
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How is the distribution of the received signal affected if the transmitted signal is changed from complex Gaussian to PSK

Suppose the received signal is $y(n) = h_0s(n)+w(n)$----(1) Where $h_0, s(n), w(n)$ all are distributed as zero mean complex Gaussian. Thus I know that $y(n)$ will also have the same distribution. If $...
paru's user avatar
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understanding the distribution of received signal

In one of the research paper following equations are given : $y(n) = h_0s(n)+w(n),d = 0$ $y(n) = h_1s(n)+w(n),d = 1$ where $n$ ranges from $1$ to $N$ and $h_0,h_1$ are wireless channel assumed as $\...
paru's user avatar
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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 ...
paru's user avatar
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2 votes
2 answers
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 ...
KMC's user avatar
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1 answer
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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
Parveen's user avatar
-1 votes
1 answer
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 ...
Abhi's user avatar
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1 vote
1 answer
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 ...
JordenSH's user avatar
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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 ...
Izzo's user avatar
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1 answer
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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 ...
7E10FC9A's user avatar
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2 votes
0 answers
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 ...
itonia.x.i's user avatar
2 votes
1 answer
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"...
AChem's user avatar
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3 votes
2 answers
2k views

Power Spectral Density from Probability Density Function

The samples of a signal $x[n]$ are i.i.d. and follow a triangular pdf with $a = 0,\ b = 2,\ c = 1$: The DC-power of the signal is $$\mu_x^2 = \big(\mathbb{E}(X)\big)^2 = \left(\int_{-\infty}^{\infty} ...
Phobos's user avatar
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1 answer
138 views

Oversample or undersample correlated noise?

I wish to measure nontrivial (non-Gaussian) broadband current noise for its distribution and power spectral density. The noise is amplified (with transimpedance amplifier) with some characteristic ...
Alexander's user avatar
  • 101
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1 answer
396 views

How to get info (mean,std) out of normplot in matlab?

Lets say we have the following data and then we have a normplot: load census; h=normplot(cdate); [mean std]=normfit(cdate); I know i can get the mean(1890) and ...
BandW's user avatar
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0 votes
1 answer
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Fit Rice Distribution for negative RSS

I measured the Received Signal Strength in dBm between a receiver $R_x$ and a transmitter $T_x$ at different distances $d_1, d_2, \dots, d_n$, and all the values that I obtained are (of course) ...
CipherX's user avatar
  • 107
-1 votes
1 answer
126 views

Bandwidth and probability of continuous signal

I'm a little bit confused as to how to calculate the bandwidth of a signal. A question has me believing that it is correlated with the probability distribution. I am however not sure of this. ...
Augustin Roegiers's user avatar
1 vote
1 answer
53 views

Plotting a density function

I am trying to plot the following function in MATLAB $$f(x) = \lambda e^{-\lambda(x-\Delta)}w(x-\Delta) $$ where $$w(x) = \begin{cases} 1 &x \geq 0 \\ 0 & {\...
user367640's user avatar
1 vote
3 answers
755 views

Why is the median of a PDF not always equal to the mean? [closed]

When studying probability density functions(PDFs), the focus is often placed on the "mean" and not the "median". The mean is often described as the center of mass of the PDF. I've always taken this as ...
Izzo's user avatar
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4 votes
3 answers
12k views

What Do Skewness and Kurtosis Represent?

I understand that the question could mean a lot of things but I am thinking specifically to image processing. For example, I know that the mean can be a basic texture feature that represents the ...
user1167596's user avatar