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

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43 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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15 views

Question on stationarity of a time series

The whole foundation of discrete Wiener theory for estimation of signals, leading to the Yule-Walker equations assumes stationarity of the time series. But, financial data, in general, may not be ...
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19 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
16 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
36 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
20 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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0answers
18 views

On the confidence intervals of matrix autocorrelation

Considering the case of signal autocorrelation in 1D, I've read that the distribution of the correlation coefficients $r$ of a white noise (independent and identically distributed random variable) ...
1
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1answer
39 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 ...
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2answers
66 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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0answers
35 views

Spatial Correlation Matrix

I have been studying the Minimum Variance Distortionless Response beamformer, and I've come to find I don't understand the spatial correlation matrix as given. For clarity, consider the output of a ...
1
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2answers
59 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 ...
0
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2answers
106 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 ...
1
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2answers
37 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
34 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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0answers
25 views

Why is ICA whitening code not giving results?

i am trying to implement FAst ICA for my project, but i am facing it hard to just go through the fisrt step. The code that i am using in matlab is as given below for ex ...
0
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1answer
58 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
103 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 ...
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0answers
6 views

Help with modeling 1-dimensional pixel profiles to test for a significant difference

I am trying to compute whether two fluorescence profiles are significantly different from each other (say between treatment 1 and treatment 2). For computing the profiles, I simply measure multiple ...
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0answers
68 views

Estimate standard deviation of random-walk using Kalman filter

I'm new to Kalman filters so this might be a stupid question. I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a ...
0
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1answer
88 views

Received signal error vs. BER

It is my understanding that the least squares algorithm (e.g., in equalization) minimizes the received signal error. However, minimizing the received signal error does not necessarily equate to ...
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1answer
205 views

The Distribution of Filtered Gaussian White Noise

Suppose I have some time series $s(t)$ which contains Gaussian white noise generated by a distribution $N(0,\sigma^2)$ Then I apply a filter to s(t) with a frequency response $H(\omega)$, giving me $...
5
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2answers
135 views

Difference between $\mathbb{E}[\mathbf{x} \mathbf{x}^{\rm{H}}]$ and $\mathbb{E}[(\mathbf{x}-\boldsymbol{\mu}) (\mathbf{x}-\boldsymbol{\mu})^{\rm{H}}]$

Let us have a random vector $\mathbf{x} \sim \mathcal{CN} (\boldsymbol{\mu}, \boldsymbol{\Sigma})$ with $\boldsymbol{\mu} \neq \mathbf{0}$. What can we say about the relationship between the elements ...
2
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2answers
62 views

Histogram Counts of a 2d Matrix

I am currently working on a project in which I have a 10 x 2 matrix: A. I want to find the top 3 number of occurrences of each row using MATLAB. ...
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1answer
395 views

what does it mean to have a decorrelated colour space?

I'm working on the problem of colour transfer between images. In the literature there's a common practice that consists in performing the transformations on images in what is called a decorrelated ...
2
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2answers
984 views

Capacity of cascade binary symmetric channels

Let's imagine that we have interconnected in cascade $L$ binary symmetric channels each with the same transition probability $p(y|x) \in \{p, q=1-p\}$, where the output of each BSC is connected to the ...
3
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1answer
64 views

Combining different Likelihoods - Particle Filter

I am new to particle filters and have a problem when it comes to the weightening (using SIR to be precise). The problem is that my different state-variables are subject to different noise-...
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0answers
21 views

Distribution of a ultrasonic signal response

I have a data set that contains ultrasonic signal responses from a cylindrical structure. I would like to characterise the distribution of these data sets. What is the best way to extract the ...
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0answers
198 views

How to detect overall error between two signals and also track changes occurred

I need to develop an algorithm that will compare two signals (1 Reference Signal and other is measured signal values from sensor) and generate some metric(s) to describe changes between them. I am not ...
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0answers
73 views

How can I use signal processing techniques in modelling noise, which doesnt follow a specific pattern

I want to take your guidance in modelling noise which is truly random. Please see below the following 2 images. First one shows my development. The background curve is the amount of solar ...
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3answers
70 views

How to apply statistical algorithms of signal processing to 'regulate' variation of a curve?

Below I am posting 2 graphs. I want to regulate the curvature of first graph using some statistical methods such as use of standard deviations, and modulate my graph to look like second one. I am not ...
1
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1answer
439 views

Can we calculate moments (mean, var, skewness, kurtosis) of a signal in frequency domain?

The computation of the mean, variance, skewness and kurtosis of a time series in the time domain is straightforward from their ...
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0answers
19 views

Use low freq signals to explain high freq response in regression

Suppose I have a number of low frequency signals, $x_1, x_2, \dots, x_n$, each of which is associated with frequency $w_1, w_2, \dots, w_n$. And I want to explain a random signal with frequency $w_r$, ...
3
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1answer
85 views

Standard deviation is varying with change in amplitude of DC signal

I am trying to make sense of the below code. I am taking a large sample so that I get good estimates for standard deviation. ...
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0answers
25 views

Kalman Filter - Gaussian representation

I'm trying to understand well the kalman filter, as a result i'm having this question : Why do we represent noise with a Gaussian ? what does this really mean intuitively ?
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1answer
59 views

Equivalence between noise covariance of real and complex models of received signal

I have a question on the equivalence of two models (complex vs. real) of a received signal in ISI channel. Yet its simplicity, I am a bit confused. Model #1: Complex Assume we transmit a complex ...
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0answers
227 views

Wiener filter yielding negative MSE (and MMSE)

I implement a Wiener filter using the following code ...
6
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2answers
163 views

Regression vector size for prediction, reconstruction and filtration with adaptive filters

I am working with adaptive filters and similar adaptive models (mainly with gradient adaptation) for a few years. I and my colleagues always struggle to find out the correct size of regression vector. ...
0
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2answers
97 views

Help in proper notations and mathematical formulation

For a given series, $S = \{-1,0,-2,1,etc\}$. The number of elements in $S$ is $N = 100$. Each $s_i$ belongs to a alphabet from a finite alphabet set $\mathcal{A} = (a_1=0, a_2=1, a_3=2, a_4=3, a_5=-1,...
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0answers
49 views

Variance and Co-variance of a Linear Forecast

Consider a linear forecasting problem where all shocks $\{\epsilon_i\}_1^n$ are independently distributed with $\epsilon_i\sim N(0,\sigma_i^2)$ for all $i$. Suppose you want to forecast $\theta = \...
0
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1answer
213 views

Variance of correlated noise

I think this is an easy question but I am confused about the answer. Assume we have correlated noise distributed as $$n \sim \mathcal{N}(0,\sigma^2 \:A),$$ where $A$ is a given square matrix. If we ...
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2answers
454 views

How to test if error has zero mean?

I know how to calculate the mean of a data set. In DSP, I think zero-mean should means that the error fluctuates around zero, and the mean of errors at any interval is zero. So what about the error in ...
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2answers
127 views

How do I know quantitatively if the correlation of two time series is significant?

I computed the correlation coefficient of two time series of daily observations, x and y, but noticed that the more sampling ...
3
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0answers
33 views

Is there any method/algorithm to estimate the magnitude of non-stationarity in a signal?

e.g. the global Lyapunov exponent can give sense of the level of chaos in the signal. Is there any reliable numerical technique to estimate "how" non-stationary (or how predictable) a signal is? Also, ...
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0answers
39 views

variance of filtered polynomial

Consider the following system: What is the variance of $y$, $\mathbb{E}(y^2)$ ? (EDIT: I know input signal has infinite power but will be made bandlimited by $H$. Both $H$ and $G$ are simple ...
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1answer
155 views

interpretation of histogram in statistical image processing

I am learning statistical image processing by myself. In papers and books, it always show the histogram of original images and gradients as the following image shows. The histograms of images vary ...
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0answers
80 views

Obtaining n values from n-1 sensors

As the questions states, lets consider we have 3 gas sensors giving me data for: A B C Note that only sensors for A and B give absolute values, yet we need the absolute values for all four species:...
5
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1answer
1k views

Cross-correlation or cross-covariance of non-zero mean signals

Cross-correlation for uniformly sampled signals is defined as [1] $$(f \star g)[n]\ \stackrel{\mathrm{def}}{=} \sum_{m=-\infty}^{\infty} f^*[m]\ g[m+n].$$ Cross-covariance for wide-sense stationary (...
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1answer
137 views

Independence of Noise at Each DFT Output

My math may be a little rusty, so I would like confirmation or correction or my calculations here. Given white noise samples, $x_i$, which are IID and zero-mean, and variance $\sigma^2_x$. I want to ...
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78 views

Received signal envelope PDF to power PDF [Wireless Communications]

I am deriving the probability density function (pdf) of the received wireless signal envelope in multi-path fading channels. I wish to transform this envelop PDF to the power PDF of that signal. I ...
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1answer
54 views

Discrete entropies

I've been given a problem where I need to find the entropy of two random variables. I can find part of the answer, but not all of it. I am given the following: $X$ is a uniformly distributed random ...