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Questions tagged [statistics]

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

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1answer
645 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
192 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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440 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
245 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
973 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 ...
2
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1answer
418 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
137 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
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
259 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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2answers
117 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
599 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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0answers
214 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
165 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
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0answers
529 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
845 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 ...
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3answers
264 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: ...
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2answers
95 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
373 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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2answers
706 views

Normalized cross-correlation in detail

I'm trying to implement a normalized cross-correlation algorithm but I don't get what in fact is this measure. What confuses is the wikipedia definition: $\frac{1}{n} \sum \frac{(f(x,y)- \overline{f})...
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2answers
1k views

FFT, How to decide if there is a signal among noise?

I have sets of data of different deep sky objects. My job is to check for any periodicity. I use IDL to run an FFT and wavelet methods to check for a signal. To test my code I ran the IDL built in ...
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0answers
193 views

Random signal modeling with Matlab

I want to build a detector of sorts. Say I have a bunch of signals and they all share some patterns, like some peaks in frequency or something more complicated that I can't bother to calculate by hand....
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1answer
675 views

Error Propagation through an IFFT

I'm not sure how to approach this problem. I will describe what I am trying to do, and what some of my matlab outputs look like. I'm not trained in signal processing or anything, so please be ...
2
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1answer
445 views

Why does circular symmetry of complex envelopes mean that $\mathbb{E} \Big[\mathbf{x}[i] \mathbf{x}^T[i] \Big] = \mathbf{0}$?

I am making my way through this paper here, and I understand everything up to equation 16, and I am stuck here. Long story short, the vector $\mathbf{x}[i]$ here is an $N$ by 1 vector, consisting of ...
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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
3k views

Magnitude-squared Coherence calculation inconsistence

I have to calculate the magnitude-squared coherence (MSC) between two signal. However, using a routine that uses only one taper (or no tapers at all) my result is always 1, despite the signals are ...
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4answers
5k views

ICA - Statistical Independence & Eigenvalues of Covariance Matrix

I am currently creating different signals using Matlab, mixing them by multiplying them by a mixing matrix A, and then trying to get back the original signals using FastICA. So far, the recovered ...
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1answer
789 views

Fisher ratio or F_ratio

I am confused while writing code to implement Fisher’s F-ratio. Suppose I have 4 speakers, each speaker pronounces 2 words and each word has 3 frames and each frame has 30 sub-bands. $u$ is mean of ...
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1answer
2k views

what is probability density function (PDF) of periodic signal

anybody knows what is the best pdf for periodic signal ? I have signal with 480 samples (16000*0.03=480) but I could not find the exact pdf for that. sometimes it appear like 2 mixed Gaussian.
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2answers
225 views

Scatter plot: calculate box where 80 % of the points are

I've a scatter plot with x- and y-axis. Now I want to calculate a rectangle which displays where 80% of the points in this plot are. I'm not very familiar with statistics, so I don't know the method ...
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1answer
2k views

Amplitude calculation

I've got an array of different values representing the y-values in a plot: ...
0
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2answers
170 views

Expected value of a Delta function times a function

I have a output signal $Y(t)= \sum_{n=-\infty}^{\infty} Z_n \delta (t-n\tau) h(t)$ and $Z_n$ is a random variable with equal probability to be $+-1$ and h(t) is $sinc(\frac t {\tau})$ and the ...
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1answer
114 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 ...
4
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0answers
111 views

Relative beat detection for two audio recordings

I'm trying to synchronize (overlap) two audio recordings of the same song: a complete HQ version, and an incomplete, noisy version (phone recording for example). The noisy recording may have had its ...
2
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1answer
488 views

Signal Processing in Amateur Radio Astronomy

I am an amateur astronomer and I took recent interest in Radio astronomy and I am also new to Digital Signal Processing. My team is trying to build a radio telescope. I am interested in the data ...
4
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2answers
960 views

Can Kalman Filter be used to track Randomly Moving Target?

i want to track random moving object with a camera using kalman filter...i have the following questions... Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ is ...
3
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1answer
135 views

Characterizing real-time sampled signal

I have a signal which is sampled in real-time. At every time interval I receive a value. I need to characterize this signal as active or inactive (to take priority in the control actions). By active ...
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0answers
59 views

Statistical Signal Analysis - what to read [duplicate]

Possible Duplicate: Introduction to Statistical Signal Processing Currently I am doing an (undergrad) class on statistical signal analysis, but I find the reader at hand (no book, buh) very hard ...
2
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0answers
64 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 ...
3
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3answers
599 views

How to estimate the mean of a clipped signal?

An accelerometer is used on a high vibration environment (a bicycle) to measure gravity. The signal clips, so data higher than a clipping value is clamped to that value. So, simply filtering the ...
6
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1answer
320 views

How to discern the distribution function of mean-squared coherence values?

This probably walks a fine line between Cross Validated and this site, but I think the practical application of it lies more on the signal processing side. I have had the occasion to record some EEG ...