Questions tagged [statistics]

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

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2answers
504 views

What does the frequency axis of a Power Spectral Density mean?

I have never really understood what the frequency axis meant when we plot the Power Spectral Density(PSD). Does it correspond to frequency as we get after we take the Fourier Transform of a time ...
2
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1answer
365 views

Detection of sine signals with random amplitudes

Problem statement: I am designing a NP detector for the following detection problem: $\mathcal H_{0}: x[n] = A_0\cos(2\pi f_0n) + w[n]$ $\mathcal H_{1}: x[n] = A_1\cos(2\pi f_0n) + w[n]$ where: $...
2
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1answer
585 views

Subsample Time Delay Estimation

Often we need to estimate the time difference of arrival between two signals to find the location of a target. Many algorithms gives the time delay corresponding to a sample number or time delay is a ...
2
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1answer
648 views

Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an ...
2
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2answers
103 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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1answer
78 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-...
2
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2answers
424 views

Features of a non-periodic signal for comparison

I am looking for comparing a signal (256 / 512 point discrete | non-periodic ) (obtained after extracting some features from the captured image) with a database of around 5000 signals (256 /512 point ...
2
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2answers
842 views

Why is autocorrelation used without normalization in signal processing field?

According to the wikipedia(Link), autocorrelation has two definition. In statistics, the definition of the autocorrelation between times $s$ and $t$ is like the following: $$\displaystyle R(s,t) = \...
2
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1answer
403 views

How to detect quadrilaterals in a point cloud?

How can I detect a quadrilateral in a point cloud that looks almost like a rectangle? How do I set the criteria (i.e orientation, size etc) to get the shape for example in the image below?
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0answers
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 ...
2
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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)....
2
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0answers
44 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
83 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:...
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0answers
55 views

Eigenvalues of correlation matrix which have the form of an harmonic function [duplicate]

As a continuation to this question, I took the matrix $C_{2 \times 2}$ which is: $$C=\left[ \begin{array}{} a& ace^{-\frac{|\phi_1-\phi_2|}{2}}\\ ace^{-\frac{|\phi_1-\phi_2|}{2}} &...
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0answers
211 views

Distribution of a signal covariance matrix

A common estimation problem in signal processing assumes the following signal model \begin{equation} \mathbf{r} = \sum_{i=1}^{Q}\alpha_i\mathbf{s}\left(w_i\right)+\mathbf{n} \end{equation} where $\...
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0answers
68 views

DSP, Related Math, Statistics, and Jitter Primers [closed]

I'm a CS who took an internship at an EE shop, and I'm trying to do some work developing in house and client applications for a chip designer, and I'm having some fundamental communication problems. ...
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0answers
65 views

Predicting Positional Displacement with a Bivariate Gaussian Distribution

In my computer-vision problem, a blob can move either forward or backwards (with a slight chance of moving sideways) along its directional axis. I am seeking a bivariate model because I need to ...
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3answers
4k views

How can a signal have no DC component

I am reading a nice book on DSP The Scientist and Engineer's Guide to Digital Signal Processing It mentions In electronics, the mean is commonly called the DC (direct current) value. How can ...
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1answer
373 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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2answers
624 views

Maximum likelihood estimator for multiplicative Gaussian noise

So I'm trying to derive an analytical solution for a MLE that should estimate a static value polluted by multiplicative Gaussian noise. The vector of measurements $\tilde{\boldsymbol{d}}$ is given as ...
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3answers
287 views

Study Signal Processing

I'd Like to ask two questions : What is the difference between studying Signal processing (both Deterministic and statistical) in Department of Electrical Engineering versus Department of Mathematics ...
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2answers
109 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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2answers
109 views

On computing the number of independent values from a signal's bandwidth?

Can anyone help me understand where the value of $2$ comes from in the following statement? ...
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1answer
643 views

How to compute the statistics of the DFT of correlated noise?

I would like to know how to compute the statistics of the discrete Fourier transform of a noise signal. To illustrate what I mean, I will first explain in detail a computation I have managed to do ...
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1answer
118 views

Establishing the function of a decaying signal

I have a set of samples from a signal. The signal is erratic in behaviour at the beginning but then it settles down and oscillates around the value of 100 (the frequency of oscillation is not ...
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1answer
131 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
90 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 ...
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1answer
1k 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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3answers
223 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
763 views

What Do We Expect Likelihood Function to Be 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 ...
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3answers
354 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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1answer
156 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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1answer
91 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
522 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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1answer
149 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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2answers
2k 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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1answer
60 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 ...
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1answer
69 views

Why are the observation features of an HMM-based recognition/synthesis system modeled by a Gaussian distribution?

Why are the observation features (namely MFCCs) of an HMM-based recognition/synthesis system modeled by a Gaussian distribution? Even the state duration is modeled by a Gaussian in this paper: K. ...
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1answer
1k views

Expected value of signals

If I have two signals $x$ and $y$ and this expression $E\{x[n]y[n-k]\}$, what is the expected value of the product? I have a basic understanding of EV based on probability, such as $$E[X]=\sum_{i=1}^{...
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1answer
174 views

Unsupervised learning algorithms to detect anomaly in waves

I have a sample of graphs (more than 10000...). that look like in the image below: I am searching for an unsupervised learning algorithms that can help me to detect anomalous observations. Here what ...
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1answer
2k views

Amplitude calculation

I've got an array of different values representing the y-values in a plot: ...
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0answers
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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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
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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0answers
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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0answers
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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0answers
433 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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0answers
541 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
53 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 = \...
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0answers
41 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 ...