Questions tagged [probability-distribution-function]
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43 questions
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Handling Summation in Autocorrelation Function for PAM Signals with Random Shifts
I am working on the autocorrelation function of a Pulse Amplitude Modulated (PAM) signal, which is given by:
$$
X(t)=\sum_{n=-\infty}^{\infty} A_n p(t-n T-\phi)
$$
where:
$A_n$ are i.i.d. random ...
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Realistic probability density function (pdf) for Radar measurement noise
Edit 1: A few tangential questions are posed in this question to get community help
Radar: FMCW | Measurements: Bearing angle, range, and range rate | Application: Aircraft/ship surveillance
Example ...
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Determination of signal amplitude distribution
For context, this figure from the reference Figure 1 of paper [1] shows, producing a signal amplitude probability generation.
When the distance $\Delta x$ is infinitely small, the probability
density ...
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Probabiliy density (Histogram) of measured data
The measured data from a gas sensor measurement system, in the absence of any excitation is as shown below. The data set consists of n = 65535 samples.
The sensor output is discretized by the ...
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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 ...
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83
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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 ...
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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 ...
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287
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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 ...
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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 ...
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130
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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 ...
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70
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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 ...
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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 ...
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124
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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.
$$ U_m \sim \mathcal{N}(\mu, \sigma) $$ ...
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139
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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 ...
- 99
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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 ...
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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}}^{-...
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98
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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 ...
- 618
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3
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64
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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 ...
- 3,595
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45
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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 ...
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279
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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., ...
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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 ...
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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 ...
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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 ...
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377
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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 ...
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2
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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 $...
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130
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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 $\...
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79
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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 ...
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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 ...
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83
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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
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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"...
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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
$$\mu_x^2 = \big(\mathbb{E}(X)\big)^2 = \left(\int_{-\infty}^{\infty} ...
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Oversample or undersample correlated noise?
I wish to measure nontrivial (non-Gaussian) broadband current noise for its distribution and power spectral density.
The noise is amplified (with transimpedance amplifier) with some characteristic ...
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1
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401
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How to get info (mean,std) out of normplot in matlab?
Lets say we have the following data and then we have a normplot:
load census;
h=normplot(cdate);
[mean std]=normfit(cdate);
I know i can get the mean(1890) and ...
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1
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131
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Fit Rice Distribution for negative RSS
I measured the Received Signal Strength in dBm between a receiver $R_x$ and a transmitter $T_x$ at different distances $d_1, d_2, \dots, d_n$, and all the values that I obtained are (of course) ...
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Bandwidth and probability of continuous signal
I'm a little bit confused as to how to calculate the bandwidth of a signal. A question has me believing that it is correlated with the probability distribution. I am however not sure of this.
...
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1
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Plotting a density function
I am trying to plot the following function in MATLAB
$$f(x) = \lambda e^{-\lambda(x-\Delta)}w(x-\Delta) $$
where
$$w(x) =
\begin{cases}
1 &x \geq 0 \\
0 & {\...
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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 ...
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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 ...
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