Questions tagged [statistics]
Statistics is the study of the collection, organization, analysis, and interpretation of data.
170
questions
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0answers
97 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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0answers
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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0answers
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-...
1
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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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0answers
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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0answers
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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0answers
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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0answers
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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0answers
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 ...
1
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0answers
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....
1
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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 ...
1
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0answers
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 ...
0
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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 ...
0
votes
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 ...
0
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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})...
0
votes
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 ...
0
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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 $...
0
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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 ...
0
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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-...
0
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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.
...
0
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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 ...
0
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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, ...
0
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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....
0
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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 ...
0
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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 ...
0
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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 ...
0
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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\}}}$$ is the channel ...
0
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1answer
331 views
Problem understanding the Expectation Operator
I know that the Expectation Operator $E\{x\}$ four discrete values is
$$ \sum_k \alpha Pr(x = \alpha_k)$$
and its very intuitive when speaking out a formula which contains the Expectation Operator. ...
0
votes
1answer
183 views
Why doesn't law of large numbers apply to this stationary time-series?
There's a paragraph in Wikipedia that states the following:
Let Y be any scalar random variable, and define a time-series $\{X_t\}$, by
$$X_{t}=Y\qquad {\text{ for all }}t$$
Then $\{X_t\}$ is a ...
0
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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 ...
0
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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 ...
0
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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 ...
0
votes
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,...
0
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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 ?
0
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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?
0
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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 ...
0
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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 ...
0
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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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0answers
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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0answers
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 ...
0
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0answers
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)...
0
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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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0answers
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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0answers
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 ...
0
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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 ...
0
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0answers
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(-...
0
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0answers
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 ...
