Questions tagged [statistics]

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

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57 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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1answer
103 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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0answers
61 views

Solving an Array Signal Processing Estimation Problem based on the Rayleigh Quotient

The Rayleigh quotient for a covariance matrix $\mathbf{C}$ and a non-zero steering vector $\mathbf{a}$ is given by $$ R(\mathbf{C},\mathbf{a}) := \frac{\mathbf{a}^H\mathbf{C}\mathbf{a}}{\mathbf{a}^H\...
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1answer
24 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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0answers
27 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
25 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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0answers
43 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
117 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 ...
4
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1answer
2k views

What is a good distance measure for matching SIFT descriptors depending on the distribution of their noise?

I have read some papers about distance measures like Euclidean, Manhattan or Chi-Square for matching gradient based image descriptors like those computed from the SIFT Algorithm (128-D vectors). Most ...
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1answer
39 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
183 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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1answer
24 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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1answer
58 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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3answers
2k views

What Does It Mean Exactly When Two Parts of a Signal Are Correlated?

I stumble quite often upon the notion that two or more parts of a signal are correlated to describe semi-formally that they belong together. For example in image processing, two pixels on an edge ...
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1answer
33 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
32 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
207 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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2answers
95 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
36 views

About the power spectrum and confidence upper limit of a time-series data

For now, I have a coupled system with 5 variables and use the Runge-Kutta method to integrate. ...
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1answer
38 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
72 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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3answers
173 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 ...
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1answer
127 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. ...
1
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1answer
152 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
46 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
25 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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7answers
6k views

Good book or reference to learn Kalman Filter

I am totally new to the Kalman filter. I've had some basic courses on conditional probability and linear algebra. Can someone suggest a good book or any resource on the web which can help me can ...
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1answer
26 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
48 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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2answers
153 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
368 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
77 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
88 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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3answers
136 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
205 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 ...
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1answer
481 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 $...
4
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2answers
143 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
97 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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3answers
316 views

comparison between frequency offset estimators

I have been working frequency offset estimation in OFDM. The objective was to compare different frequency offset estimation techniques. By using MATLAB, I have simulated three different estimation ...
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3answers
75 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 ...
2
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1answer
775 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
2k 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 ...
1
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1answer
689 views

What do we espect Likelihood function used for?

In my understanding, I let make a example. For example, you can see in the following picture. Consequently, We want to find ^sigma. and We have already known the observation data(which is random ...
2
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1answer
74 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-...
10
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0answers
1k views

Ensemble learning, multiple classifier system

I am trying to use a MCS (Multi classifier system) to do some better work on limited data i.e become more accurate. I am using K-means clustering at the moment but may choose to go with FCM (Fuzzy c-...
1
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0answers
328 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 ...
1
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1answer
751 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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1answer
6k views

What does standard deviation of noise 1 mean?

In theory of noise,Typically, the standard deviation of noise has 1 and mean has 0. I think that the reason of noise mean has 0 that we can assume that all noise signal go to zero when we sum it all. ...
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0answers
1k views

4th order cumulant of signal

I'm trying to implement some code for watermarking on audio based on a scientific paper. I'm stuck in the part of the pseudo code where they calculate the fourth order cumulant of the approximation ...
2
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1answer
110 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. ...