Questions tagged [statistics]

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

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273 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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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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1answer
2k 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
144 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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87 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
59 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
328 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 ...
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2answers
503 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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0answers
39 views

Optimize online weighted kurtosis algorithm

I am currently working on a Simulink block designed to perform an online computation of the weighted kurtosis typical of a certain signal. This block is part of a larger control algorithm, which will ...
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1answer
334 views

Determining the covariance of point clouds in real-time

So basically I have a set of multidimensional data that I need to determine the covariance of between dimensions in real-time. Each point that comes in is a vector. I have gotten the mean and variance ...
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1answer
448 views

How is cross-correlation related with orthogonality?

In linear prediction we can say that in case of optimum linear predictor the error with be orthogonal to data. And when we derive minimum mean square error for $\underline{y} = \mathbf{a}\underline{x} ...
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2answers
376 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 ...
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2k views

Why is Gaussian noise called so?

Can you please explain: why is a specific type of noise called "Gaussian noise"? Why is it relevant to call it Gaussian? Please, explain in layman's terms.
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47 views

Pearson correlation of neural responses with it's linear estimation

I am trying to understand the following fact from this article (page 13): How can single neurons predict behaviour Suppose I have a linear estimation of a stimulus: $ \hat{s} = \mathbf{w}^T(\mathbf{r}...
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34 views

How can a medical doctor use the information given by someone working in medical image computing(shape analysis)? Details follow

Posted also here, where it's been put on hold. I did modify it afterwards though. https://biology.stackexchange.com/questions/43997/how-can-a-medical-doctor-use-the-information-given-by-someone-...
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1answer
303 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: $...
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2answers
640 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) = \...
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35 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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1answer
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This is an expression for the computation of kurtosis.

However, I don't understand what the subscript '4x' or the parameter (0,0) stand for. Could anyone explain ?
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1answer
65 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
379 views

How do I interpret these autocorrelograms?

Hello signal processing wizards. I am young and feeble, and would like some help interpreting my spike-train autocorrelograms of six isolated neurons. These histograms were created using the code ...
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1answer
133 views

adjust mean of signal using exponential

I have discrete signals whose values are between 0 and 1. I wish to post-process such a signal such that the mean of its values equals 0.5, yet keeping maximum and minimum values 0/1 intact. ...
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1answer
356 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 ...
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1answer
1k views

What is the connection between analog signal to noise ratio and signal to noise ratio in the IQ plane in a quadrature demodulation system?

We would like to compute the quantitative relation between analog noise near the LO frequency and the statistics of points found in the IQ plane after IQ demodulation. In order to completely ...
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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
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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1answer
56 views

I'm looking for the concept about estimated standard deviation

I am looking for the concept about estimate standard deviation. Actually I'm not sure how can I get a concept the estimate standard deviation ? If you know the concept, then would you let me know ...
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1answer
69 views

What does it mean when one model fit the data better than does a comptitor model?

I'm trying to review MLE (maximum likelihood estimation). What does it mean when one model fit the data better than does a comptitor model?
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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 ...
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2answers
542 views

Filtering random Signal

My question is easy one actually. First, I generate a random signal using randn() function of MATLAB like this: Then, I design a FIR filter of order 200 of pass-...
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1answer
622 views

What is bispectrum?

I am working on a project that uses EEG signals of the brain to identify emotional states. While surveying the literature, I came across several references where "derived features of bispectrum" are ...
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0answers
183 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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1answer
169 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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0answers
427 views

Are discrete wavelet transform based statistical features invariant to rotation/translation/scale?

I'm reading a paper where image classification is done. Their approach is to use the discrete wavelet transform with bi-orthogonal wavelets of degree 3.5 and decomposition of level 3 on images. Based ...
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3answers
235 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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1answer
873 views

Fixed SNR with unitary noise variance

I've just one question : How can I write a model like y = x + w,( with w a white gaussian noise) with a fixed SNR and a noise variance equal to 1. What coefficient may I have before x ? Thanks !
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1answer
3k views

What is a covariance matrix?

Suppose you have k samples from each of the N elements of a uniform linear array (ULA) of sensors: What is the physical meaning of a covariance matrix? How do you form a covariance matrix with the ...
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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 ...
2
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1answer
391 views

Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary process in time (in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary ...
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0answers
126 views

The autocorrelation of a WSS process as a linear operator

If I'm given a autocorrelation matrix of a WSS process what interpretation should I put on the resulting vector. More concretely the matrix takes the form $\begin{bmatrix} x_1 & x_2 & \...
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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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0answers
34 views

Statistics of the output of a high bitrate signal filtered through a narrow band low pass filter

I was wondering what would be the statistics of the output of the filtering of an extremely wideband signal (e.g. 10 Gbps random data stream) through a narrowband low-pass filter (e.g. 10 MHz LP). I ...
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1answer
227 views

What is the mean power of a complex random variable?

Say $\alpha$ is a complex random variable, then which one of the following expressions is correct? $\mathbb{E}[\alpha^2]$ or $\mathbb{E}[\alpha \alpha^*]$?
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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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2answers
108 views

Measure of intermittency/continuousness of a signal

I have three signals (below) each having the same standard deviation, however, are clearly very different temporally. Is there some such metric that could be calculated for each of these signals to ...
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1answer
540 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 ...
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0answers
66 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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209 views

Yet Another Peak Detection Request

I looked over the other entries regarding peak detection and none seem to answer my question. I'm working with Fourier spectra of digitized audio that can't be measured again. There are no ...
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0answers
520 views

Constant amplitude, uniform phase - what's the distribution of the complex signal then?

The well-known relationships for zero-mean circularly-symmetric complex Gaussian $z = a + jb = |z| \exp(j\varphi)$ signals are the amplitudes $|z| = \sqrt{a^2 + b^2}$ are Rayleigh-distributed the ...
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1answer
812 views

wiener filter (non-causal) calculating covariance matrices

I'm learning about the Wiener filter, and I'm working on my own implementation. I'm starting out with the non-causal filter, and I need to calculate some covariance matrices. If the signal is assumed ...