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

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5
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1answer
152 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} ...
2
votes
2answers
126 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 ...
6
votes
2answers
660 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.
1
vote
0answers
37 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} = ...
1
vote
0answers
21 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. ...
2
votes
1answer
175 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: ...
0
votes
0answers
15 views

question about prior in bayesian image processing

I am learning bayesian image processing. Bayesian approach will take prior knowledge about image into account. From one material, it says knowledge is expressed via probability functions. I understand ...
3
votes
2answers
84 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) = ...
0
votes
0answers
38 views

Separating two mixed signals where one is constant (SVD/ICA)

I have two measurements m1 and m2 which contain a mix of two sources (signal + error). Typically this problem can be solved using SVD or Independent Component Analysis which will chose principal ...
1
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0answers
28 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}} ...
0
votes
1answer
41 views

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 ?
1
vote
1answer
30 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. ...
0
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0answers
44 views

sklearn - two gaussians fit

I have some data here : http://pastebin.com/q3ncX6yM, the histogram of which I am trying to fit with two gaussians following ...
0
votes
1answer
69 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 ...
2
votes
1answer
115 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. ...
0
votes
0answers
13 views

How can you test Gamma in ISP for test?

In CMOS image sensor, there are gamma processing block in the so many ISP chains. Is there any one know how to test the gamma block only whether working good or something wrong? How can you test ? Is ...
1
vote
1answer
71 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 ...
4
votes
1answer
263 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 ...
1
vote
1answer
142 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 ...
0
votes
0answers
20 views

How do probabilities inform recognition and prediction?

This question is a broad one but a connection I have been trying to wrap my head around. I have been doing statistical inference like anova and regression (linear and logistic) along with some basic ...
0
votes
0answers
53 views

What is difference noise reduction technic on additive gaussian noise and poisson noise?

As I know the camera noise are consisting like poisson noise and additive gausian noise. I want to know about What is difference noise reduction technic on additive gaussian noise and poisson noise? ...
-1
votes
1answer
214 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. ...
0
votes
1answer
46 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 ...
0
votes
1answer
50 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?
1
vote
1answer
176 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 ...
1
vote
2answers
119 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 ...
0
votes
1answer
112 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 ...
2
votes
0answers
66 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 ...
1
vote
1answer
111 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 ...
0
votes
0answers
135 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 ...
0
votes
3answers
146 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 ...
0
votes
1answer
295 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 !
2
votes
1answer
189 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 ...
6
votes
3answers
461 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
votes
2answers
227 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 ...
1
vote
0answers
42 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 & ...
1
vote
0answers
46 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}) := ...
1
vote
0answers
29 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 ...
0
votes
1answer
58 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 $\mathbb{E}[\alpha \alpha^*]$?
1
vote
3answers
138 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 ...
2
votes
2answers
60 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 ...
2
votes
1answer
166 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 ...
1
vote
0answers
56 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. ...
1
vote
0answers
154 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 ...
0
votes
0answers
232 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 ...
0
votes
1answer
353 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 ...
3
votes
3answers
152 views

How to determine, calculate and plot a probability distribution for a given set of numbers?

A device is rotating with a particular wind speed and producing such pulse frequencies in a minute: ...
1
vote
2answers
81 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? ...
2
votes
1answer
181 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?
1
vote
1answer
310 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 ...