Questions tagged [statistics]

Statistics is the study of the collection, organization, analysis, and interpretation of data.

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16 views

Statistics to characterize time-domain envelope of acoustic signal

I am interested in comparing 0.5-second 44100/s signals when different ADSR envelopes are applied to them. However, I don't want the comparison to be as fine-grained as simply calculating a 5000-...
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27 views

Texture Analysis and Statistic Models

Let's assume we have a random binary texture image $X(i,j)$ that comes from a Markov-Gibbs model with zero boundary conditions. The probability distribution Gibbs function is: $$Pr(X)=\frac{1}{Z}\exp(-...
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15 views

Standard Deviation of Character Gradients in a Document Image

I have the paper titled "CG-DIQA: No-reference Document Image Quality Assessment Based on Character Gradient". It is all about assessing the quality of the document image based on its blurriness. To ...
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1answer
30 views

Complex gaussian random variable [closed]

In my work i need to generate circularly symmetric complex gaussian random variables with non zero mean and certain variance in matlab. I know the command for generating in case of zero mean , but ...
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1answer
12 views

Questions in a Character Degradation Model Paper

I have questions in the ‘Noise region definition’ and ‘Noise generation process’ of the paper “A character degradation model for grayscale ancient document images”. In Noise region definition, ...
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1answer
28 views

Cepstrum of white gaussian noise

What are the statistics of the cepstrum of gaussian white noise? \begin{align}\newcommand{\Nfft}{ {N_{\mathrm{FFT}} }}\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT} x_i &\sim \...
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1answer
60 views

Derivation of Circular Mean Square Error

I would like to understand how Eq. (36) in [2] was derived: The rationale behind the definition of circular sample mean in Eq. (37) is clear, but there is no motiviation for the CMSE definition in Eq....
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28 views

What does Allan variance really means? [duplicate]

Let a sensor (e.g. accelerometer) with a combination of white gaussian noise and random walk noise. The loglog plot that is usually shown as function of a time parameter, affine decreasing for a ...
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14 views

About convergence of KL divergence: if the two probability distributions are type, does the law of large number work?

If I pick $N$ samples from $P_X$ and $P_Y$, they are two independent discrete distributions. $X_1,X_2,\ldots,X_N$ are drawn i.i.d from $P_X$, and $Y_1,\ldots,Y_N$ are drawn i.i.d from $P_Y$. I got $...
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1answer
70 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 ...
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1answer
76 views

Sum of correlated exponential random variables

How do we find PDF of sum of correlated exponential random variables. I know for independent random variables. But how to find it for correlated exponential random variables.
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2answers
59 views

Lightweight test for bimodal distributions?

Here, and in the stats stackexchange, seem to be answers that reference tests for bimodal distributions that involve iterative binning or iterative curve fitting methods. However "eyeballing" a plot ...
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1answer
31 views

Generalized Likelihood Ratio test for correlated data

Consider a sequence of random variables $\overline{z} = \{z(k-M+1), ..., z(k)\}$, with probability density depending upon a scalar parameter $\theta$. It is intended to decide between two hypotheses ...
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1answer
87 views

The expectation in power spectral density

I'm a bit confused with the definition of the power spectral density (PSD). From Wiki https://en.wikipedia.org/wiki/Spectral_density , I found the definition is: $$ S_{xx}(\omega) = \lim_{T\...
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27 views

CWT coefficients as features for ML algorithms

I use CWT coefficients as features in ML algorithms and then I did the feature selection using the chi-square test but recently I figured out that the chi-square test can only be applied for ...
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22 views

Finding the error in the total integrated intensity of a fitted 2D Gaussian

I have been trying to fit signals to a 2D Gaussian function, and while I have bene able to use sciKit-image's curve_fit function to find the covariance matrix for ...
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0answers
17 views

ICA School Project

I have been stuck on my school project that consists of independent component analysis. My code will run, but only 50-60% of the time it unmixes the signals. Another problem I have is the amplitudes ...
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1answer
66 views

Autocorrelation for Stationary Signals

I'm having trouble grasping the autocorrelation function for stationary signals, both strict stationary and WSS. First for strict sense, we have $$\forall(\tau,t_1, \ldots, t_n) \in \mathbb{R} \land ...
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1answer
202 views

Integral over power spectral density

The wikipedia entry on PSD has one confusing line: Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process) But ...
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0answers
16 views

How do I show that two sets of spectra are different?

I essentially have 6 spectral curves, 3 repeats for two samples. I want to be able to show that two samples are distinct (if they are). I have tried spearman's correlation already, which does produce ...
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1answer
273 views

How to transform data to uniform distribution (uniform percentiles)?

Given the list of data points (normalized in [0,1] range), I plot the histogram of values and compute percentiles (shown as x ticks). How to find a transformation of data values so the histogram is ...
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0answers
28 views

Test of statistical significance of power-spectrum against red-noise

I have a process which is most probably red-noise and my goal is to know if the peaks or pits are "real" or just due to random fluctuations. I would like to know if there is exists a test of ...
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1answer
90 views

Block by block CCDF and PAPR analysis in MATLAB

There are few signals (OFDM-like modulation scheme with uniformly distributed data source) generated by my script. I need to compare scheme performance in sense of CCDF (Complementary Cumulative ...
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2answers
27 views

How to sketch output PDF given the transformation?

Question: Let Random variable $X$ with $PDF$ = $f_{X}(x)$ be the input to device with input output characteristics as shown below then sketch the $PDF$ of $Y$ i.e, $f_{Y}(y)$ My attempt: for X>0 ,$...
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1answer
110 views

Calculate the Standard Deviation of Fundamental Frequency (MFCC)

I'm implementing a gunshot detector following the article "Algorithm for Gunshot Detection Using Mel-Frequency Cepstrum Coefficients (MFCC)" (paywall). In the article, the authors uses 22 features ...
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1answer
34 views

Radio Signal Stationarity

A radio signal recording of a wireless communication system (e.g: Wi-Fi traffic) is beaconized, channelized and subject to noise. When working with such an RF signal, numerically transformed to a ...
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1answer
76 views

An Interesting Model with Unknown Orthogonal Design Matrix

Suppose the multivariate one-way anova model for the raw data , i.e. $$ \label{Example_model_1} \mathbf{y}_{ij}=\mathbf{\mu}+\mathbf{z}_i+\mathbf{e}_{ij}, ~~ i=1,\ldots,m,~~j=1,\ldots,n_i,~~~~~~~~~~...
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0answers
63 views

Threshold for CAF Surface

I am calculating a time partitioned Cross Ambiguity Function (CAF) by adding the surfaces of different time-sectioned CAFs together. Meaning, I calculate a CAF using 10 seconds of IQ data, calculate a ...
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1answer
49 views

Differences in moving window rms due to sampling rate

I have a 10 second recorded signal band pass filtered from 100-500 Hz. The original sampling rate is 10 kS. Now I run a moving window RMS with a window length: 10 ms on the signal (10/1000 * sampling ...
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0answers
44 views

What is the error rate in compressed sensing?

Let $x \in \mathbb{R}^n$ be a $k$-sparse vector. Given $A \in \mathbb{R}^{m \times n}$, we have a measurement vector $y$ given by $$y=Ax$$ Let $\hat{x}$ be defined as follows $$\hat{x}:=\arg\min_{z\...
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1answer
36 views

Demonstrate the mean of the sample variance

Let's suposse I have a vector of elements $x(n) = \{x(0), x(2), \cdots ,x(N-1)\}$ from a random process X of mean $\mu_x$ and variance $\sigma_x^2$. I want to see if I can estimate the mean and ...
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1answer
42 views

Spatial diversity: symbol error probability, upper bound

I am trying to understand the calculation upper bound that is given in book. Edit 1: I added 3,44 Can someone explain to me how to come from (5.5) to (5.7) ?
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1answer
239 views

Example of non-equivalence of the two PSD definitions

According to the book Introduction to Spectral Analysis by P. Stoica and R. Moses, the power spectral density (PSD) $P(\omega)$ can either be defined as the discrete-time Fourier transform (DTFT) of ...
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1answer
47 views

Channel direction

I am reading a book called Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency, and it implies that $$\frac{\mathbf{h}}{\sqrt{\text{E}\left\{\|\mathbf{h}\|^2\right\}}}$$ is the channel ...
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1answer
106 views

State of the art algorithms for estimating noise variance

Suppose I have a signal $X[n]= f[n] + W[n]$, where $W$ is uncorrelated Gaussian white noise satisfying $E\{W[n]W[k]\} = \sigma^2 \delta[n-k]$. What are the state-of-the-art algorithms for determining ...
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1answer
275 views

Problem understanding the Expectation Operator

I know that the Expectation Operator $E\{x\}$ four discrete values is $$ \sum_k \alpha Pr(x = \alpha_k)$$ and its very intuitive when speaking out a formula which contains the Expectation Operator. ...
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1answer
299 views

Random Signals - statistical properties are time dependant?

I'm taking a course on DSP and we're being introduced to the random signals, in particular continuous time and discrete time random signals. We're told that if we repeat a single random experiment at ...
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1answer
48 views

Lower Bound of Divergence

I want to prove that a lower bound of the Divergence between two probability distributions $p$ and $q$ defined on the set $\mathcal{U}$ can be expressed by defining a subset $\mathcal{S}\subset\...
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0answers
29 views

how to robustly estimate low and up envelope of signal with trend, few level constant steps and noise

I am looking for robust estimation method of low and up envelope of the signal consisting from smooth trend component, constant steps between few fixed levels and additive noise (+ outliers of course)....
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1answer
35 views

Is it possible to classify biosignal data based on feature extraction through multiple linear regression model? [closed]

i have 16 channel 2 class motor imaginary right hand ,right leg data.IS it possible to classify this through multiple linear regression model based on feature extraction?can i classify 3 class data ...
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1answer
121 views

Why doesn't law of large numbers apply to this stationary time-series?

There's a paragraph in Wikipedia that states the following: Let Y be any scalar random variable, and define a time-series $\{X_t\}$, by $$X_{t}=Y\qquad {\text{ for all }}t$$ Then $\{X_t\}$ is a ...
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1answer
59 views

How would I fit a distribution to this image noise?

I have collected some noise data from a dimly lit CMOS image sensor. The distribution of pixel values is tallied below:- I'd like to be able to simulate this sensor noise. How would I fit a ...
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2answers
96 views

What Is a Weighted Local Histogram?

I'm reading through a couple of academic papers, and this terms often comes up "local weighted histogram". An example of quote is the following: First, cumulative histograms are built for every ...
2
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2answers
122 views

How to solve equations for the MMSE receiver?

Given the following equations for the achievable rate of the Minimum Mean-Squared Error Receiver [1]: $$\mu = \frac{1}{K-1} \sum_{i=1, i \neq k}^{K}{\frac{1}{Mpd_{i}\left(1 - \frac{K-1}{M}+ \frac{K-1}...
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2answers
289 views

Isolate High Variance vs Low Variance Sections of Signals

I have the following one-dimensional signals: The goal is to identify the sections with smaller variances compared to the rest (For Python, that is to get their index value in the array). In the ...
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2answers
588 views

pdf of the sum of gaussian distributions using fft Ask [closed]

I am trying to derive the pdf of the sum of independent random variables. At first i would like to do this for a simple case: sum of gaussian random variables. I was surprised to see that i don't get ...
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2answers
101 views

Applying the CUSUM algorithm to a correlated random process

As far as I know, the CUSUM algorithm is meant for detecting change points on discrete-time uncorrelated random processes. For instance, to apply the CUSUM algorithm to a discrete Gaussian process, ...
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0answers
160 views

What is the difference between Statistical Signal Processing and Estimation and Detection?

Looking at the syllabus of Statistical Signal Processing in different university I see a lot of correlation with that of Estimation and Detection? In some universities, these are seen the same. For ...
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1answer
231 views

Redistributing Color in a RGB Image According to a Gaussian Distribution

I haven't done this stuff in a while. If I have an image $I$ I can equalize the histogram of the image using some opencv procedure, it's already defined. Equalizing an histogram means essentially to ...
3
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3answers
186 views

Extracting common signal without knowledge about noise [closed]

Given two noisy time series thought to contain a common signal, $$ x_1(t) = s(t) + n_1(t), \quad x_2(t) = s(t) + n_2(t), $$ what is the best way to determine $s(t)$ without assuming any distribution ...