Questions tagged [statistics]

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

Filter by
Sorted by
Tagged with
1
vote
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 ...
0
votes
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 ...
1
vote
1answer
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,~~~~~~~~~~...
1
vote
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 ...
0
votes
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 ...
0
votes
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\...
0
votes
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 ...
-1
votes
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) ?
3
votes
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 ...
0
votes
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. ...
0
votes
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 ...
1
vote
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 ...
0
votes
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
vote
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 ...
-1
votes
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\...
2
votes
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)....
-1
votes
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
2
votes
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}...
1
vote
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 ...
0
votes
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 ...
1
vote
2answers
78 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, ...
0
votes
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 ...
0
votes
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 ...
3
votes
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 ...
1
vote
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 ...
0
votes
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 ...
-1
votes
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
votes
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
votes
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. ...
2
votes
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
votes
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 ...
2
votes
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-...
1
vote
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 ...
0
votes
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 ...
1
vote
1answer
752 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 ...
2
votes
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. ...
0
votes
0answers
31 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 ?
0
votes
1answer
67 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 ...
0
votes
0answers
352 views

Wiener filter yielding negative MSE (and MMSE)

I implement a Wiener filter using the following code ...
5
votes
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
votes
2answers
101 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,...
1
vote
0answers
51 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
votes
1answer
352 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 ...
0
votes
2answers
879 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 ...
1
vote
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 ...
2
votes
0answers
36 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, ...
1
vote
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 ...