Questions tagged [statistics]

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

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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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48 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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36 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
727 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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455 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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166 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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64 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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35 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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223 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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196 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
912 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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66 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 ...
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3answers
100 views

Averaging data from 2 sensors

Suppose we take a reading of a single rotating axis using 2 identical sensors. Intuitively, I think that averaging the outputs of both sensors will yield a less noisy result. But what if sensor A has ...
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1answer
507 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 ...
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2answers
572 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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2answers
786 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
174 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
43 views

Complex gaussian random variable [closed]

In my work i need to generate circularly symmetric complex gaussian random variables with non zero mean and certain variance in matlab. I know the command for generating in case of zero mean , but ...
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1answer
928 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 $...
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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 $\left(16000*0.03=480\right)$ but I could not find the exact pdf for that. sometimes it appear like 2 mixed ...
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1answer
23 views

Statistics to characterize time-domain envelope of acoustic signal

I am interested in comparing 0.5-second 44100/s signals when different ADSR envelopes are applied to them. However, I don't want the comparison to be as fine-grained as simply calculating a 5000-...
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1answer
11k 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
64 views

ML estimation - solve for x

I'm trying to solve the following maximum likelihood estimation but for multiplicative noise instead of additive noise: So the goal is to do ML-estimation for a scalar constant $x$, which is ...
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1answer
12 views

Questions in a Character Degradation Model Paper

I have questions in the ‘Noise region definition’ and ‘Noise generation process’ of the paper “A character degradation model for grayscale ancient document images”. In Noise region definition, ...
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1answer
65 views

Derivation of Circular Mean Square Error

I would like to understand how Eq. (36) in [2] was derived: The rationale behind the definition of circular sample mean in Eq. (37) is clear, but there is no motiviation for the CMSE definition in Eq....
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1answer
35 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 ...
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1answer
55 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 ...
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1answer
44 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 ...
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1answer
48 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 ...
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1answer
331 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. ...
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1answer
183 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 ...
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2answers
648 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 ...
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1answer
118 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 ...
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1answer
89 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 ...
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2answers
105 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,...
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1answer
618 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
123 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 ?
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1answer
74 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
1k 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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1answer
714 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 ...
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1answer
27 views

Intuitive definition of ergodicity for random signal

Is it possible to define the ergodicity of the random signal in an intuitive sense without using any statistical reference?
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10 views

After upscaling a signal what noise metric to use for noise qualification

If I have a 2d signal (like image) and interpolate (linear) it to get an upsampled signal, how can I qualify the noise, with which metric? STD changes between the signal and its'upsampled counterpart ...
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22 views

standard deviation of two constant noised signals related through interpolation

Let us say say we have a noised constant signal and want to evaluate the standard deviation (std) of the noise. We calculate the std of the said noised signal and call it $\sigma_1$. Now we process ...
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11 views

Applying ICA on 3rd order cumulant

Background: I was reading the article Application of Higher Order Statistics for Atrial Arrhythmia Classification, and they mentioned using the higher order cumulant $$C_3^x = m_3^x(i, j)=E[x(n)x(n+i)...
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1answer
36 views

Lower bound of weighted average of sequence

Can anyone prove that $$\mathrm{avg}\left(\frac {a_i}{\left(1+a_i\right)^2}\right) \ge \frac{\mathrm {avg}({a_i})}{\left(1+\mathrm{avg}{(a_i)}\right)^2}$$ for a sequence of positive valued elements $...
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13 views

Correlation in Image Processing vs Correlation of statistics

I am new to image processing. Please forgive me if you find this question naive or meaningless. I was studying about correlation filtering in images to smoothen the image. I want to know if ...
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13 views

Permutation test on two simultaneously recorded EEG signals

I have two EEG signals that are simultaneously recorded (and has been further synced) using two EEG devices, namely device 1 (ground truth) and device 2 (investigational device). Imagine one device ...
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0answers
8 views

Consistency check of Kalman Filter

I am interested doing the consistency check of the Kalman filter. There are several measures like Posterior Cramer Rao Lower Bound (PCRLB), NIS (Normalised Innovation Squared), NEES(Normalized ...
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30 views

Texture Analysis and Statistic Models

Let's assume we have a random binary texture image $X(i,j)$ that comes from a Markov-Gibbs model with zero boundary conditions. The probability distribution Gibbs function is: $$Pr(X)=\frac{1}{Z}\exp(-...
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17 views

Standard Deviation of Character Gradients in a Document Image

I have the paper titled "CG-DIQA: No-reference Document Image Quality Assessment Based on Character Gradient". It is all about assessing the quality of the document image based on its blurriness. To ...