Questions tagged [statistics]

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

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15 views

What's the difference between nonstationary and time varying?

I am confused by the following statement from the paper Beamforming: A Versatile Approach to Spatial Filtering by Barry D. and Kevin M.: There are two basic adaptive approach: 1) block adaption ..., 2)...
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What is the physical significance of statistical quantities like mean, variance, skewness and kurtosis of a digital signal?

I understood the mathematical meanings of the mean, variance, skewness and kurtosis. But when we calculate these quantities for a signal (say a digital audio signal), what physical meaning do they ...
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29 views

Effectively extracting “real” data from a noisy dataset

This question was originally posed to Math SE. It was suggested that DSP SE would be more suitable. Background & Motivation: I have three lists of timestamps (UNIX timestamps, plus a subsecond ...
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21 views

When is Markov a Martingale

I have two questions and I am very confused about the concepts Can a Markov process of order one also be a a Martingale? Is any Markov process of order one also a Martingale? For 1. I would say yes, ...
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25 views

Generating data with given Auto and Cross Correlations

I have two discrete vectors $\mathbf{x}_1$ and $\mathbf{x}_2$, and I'm trying to generate more data $\mathbf{f}_1$ and $\mathbf{f}_2$ that has some basics properties of $\mathbf{x}_1$ and $\mathbf{x}...
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27 views

Intuitive definition of ergodicity for random signal

Is it possible to define the ergodicity of the random signal in an intuitive sense without using any statistical reference?
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12 views

After upscaling a signal what noise metric to use for noise qualification

If I have a 2d signal (like image) and interpolate (linear) it to get an upsampled signal, how can I qualify the noise, with which metric? STD changes between the signal and its'upsampled counterpart ...
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1answer
48 views

What Are Intuitive Explanations for Shrinkage in the Context of Image Denoising?

I have occasionally come upon the term "shrinkage", mostly in the context of denoising methods. My rough understanding is that it refers to the part where the real distribution might not be ...
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25 views

standard deviation of two constant noised signals related through interpolation

Let us say say we have a noised constant signal and want to evaluate the standard deviation (std) of the noise. We calculate the std of the said noised signal and call it $\sigma_1$. Now we process ...
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11 views

Applying ICA on 3rd order cumulant

Background: I was reading the article Application of Higher Order Statistics for Atrial Arrhythmia Classification, and they mentioned using the higher order cumulant $$C_3^x = m_3^x(i, j)=E[x(n)x(n+i)...
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149 views

What will be the distribution of a given signal

Suppose I have a signal $$ \mathbf{s} \sim C \mathcal{N}\left(\mathbf{0}, \sigma^{2} \mathbf{I}_{N_{}}\right) $$ The signal going through a channel : $$ {\mathbf{r}}_{}=\mathbf{s}+{\delta \mathbf{n}} ...
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36 views

Lower bound of weighted average of sequence

Can anyone prove that $$\mathrm{avg}\left(\frac {a_i}{\left(1+a_i\right)^2}\right) \ge \frac{\mathrm {avg}({a_i})}{\left(1+\mathrm{avg}{(a_i)}\right)^2}$$ for a sequence of positive valued elements $...
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3answers
107 views

Averaging data from 2 sensors

Suppose we take a reading of a single rotating axis using 2 identical sensors. Intuitively, I think that averaging the outputs of both sensors will yield a less noisy result. But what if sensor A has ...
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1answer
65 views

ML estimation - solve for x

I'm trying to solve the following maximum likelihood estimation but for multiplicative noise instead of additive noise: So the goal is to do ML-estimation for a scalar constant $x$, which is ...
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14 views

Correlation in Image Processing vs Correlation of statistics

I am new to image processing. Please forgive me if you find this question naive or meaningless. I was studying about correlation filtering in images to smoothen the image. I want to know if ...
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13 views

Permutation test on two simultaneously recorded EEG signals

I have two EEG signals that are simultaneously recorded (and has been further synced) using two EEG devices, namely device 1 (ground truth) and device 2 (investigational device). Imagine one device ...
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Consistency check of Kalman Filter

I am interested doing the consistency check of the Kalman filter. There are several measures like Posterior Cramer Rao Lower Bound (PCRLB), NIS (Normalised Innovation Squared), NEES(Normalized ...
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1answer
23 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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30 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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17 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
45 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
57 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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69 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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40 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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20 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
129 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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173 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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69 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
53 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
189 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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29 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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23 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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18 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
104 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
644 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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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
633 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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1answer
129 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
36 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
153 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
35 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
91 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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68 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
58 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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46 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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46 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
47 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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256 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
49 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 ...