Questions tagged [statistics]

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

38 questions with no upvoted or accepted answers
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Ensemble learning, multiple classifier system

I am trying to use a MCS (Multi classifier system) to do some better work on limited data i.e become more accurate. I am using K-means clustering at the moment but may choose to go with FCM (Fuzzy c-...
5
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2answers
182 views

Regression vector size for prediction, reconstruction and filtration with adaptive filters

I am working with adaptive filters and similar adaptive models (mainly with gradient adaptation) for a few years. I and my colleagues always struggle to find out the correct size of regression vector. ...
5
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0answers
164 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. ...
4
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1answer
2k views

What is a good distance measure for matching SIFT descriptors depending on the distribution of their noise?

I have read some papers about distance measures like Euclidean, Manhattan or Chi-Square for matching gradient based image descriptors like those computed from the SIFT Algorithm (128-D vectors). Most ...
4
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0answers
109 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 ...
3
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0answers
1k views

4th order cumulant of signal

I'm trying to implement some code for watermarking on audio based on a scientific paper. I'm stuck in the part of the pseudo code where they calculate the fourth order cumulant of the approximation ...
2
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0answers
25 views

how to robustly estimate low and up envelope of signal with trend, few level constant steps and noise

I am looking for robust estimation method of low and up envelope of the signal consisting from smooth trend component, constant steps between few fixed levels and additive noise (+ outliers of course)....
2
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0answers
36 views

Is there any method/algorithm to estimate the magnitude of non-stationarity in a signal?

e.g. the global Lyapunov exponent can give sense of the level of chaos in the signal. Is there any reliable numerical technique to estimate "how" non-stationary (or how predictable) a signal is? Also, ...
2
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0answers
82 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:...
2
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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 $\...
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 ...
1
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1answer
24 views

Calculate the Standard Deviation of Fundamental Frequency (MFCC)

I'm implementing a gunshot detector following the article "Algorithm for Gunshot Detection Using Mel-Frequency Cepstrum Coefficients (MFCC)" (paywall). In the article, the authors uses 22 features ...
1
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1answer
57 views

An Interesting Model with Unknown Orthogonal Design Matrix

Suppose the multivariate one-way anova model for the raw data , i.e. $$ \label{Example_model_1} \mathbf{y}_{ij}=\mathbf{\mu}+\mathbf{z}_i+\mathbf{e}_{ij}, ~~ i=1,\ldots,m,~~j=1,\ldots,n_i,~~~~~~~~~~...
1
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0answers
27 views

Threshold for CAF Surface

I am calculating a time partitioned Cross Ambiguity Function (CAF) by adding the surfaces of different time-sectioned CAFs together. Meaning, I calculate a CAF using 10 seconds of IQ data, calculate a ...
1
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1answer
58 views

What Is a Weighted Local Histogram?

I'm reading through a couple of academic papers, and this terms often comes up "local weighted histogram". An example of quote is the following: First, cumulative histograms are built for every ...
1
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0answers
203 views

Estimate standard deviation of random-walk using Kalman filter

I'm new to Kalman filters so this might be a stupid question. I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a ...
1
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0answers
327 views

How to detect overall error between two signals and also track changes occurred

I need to develop an algorithm that will compare two signals (1 Reference Signal and other is measured signal values from sensor) and generate some metric(s) to describe changes between them. I am not ...
1
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0answers
51 views

Variance and Co-variance of a Linear Forecast

Consider a linear forecasting problem where all shocks $\{\epsilon_i\}_1^n$ are independently distributed with $\epsilon_i\sim N(0,\sigma_i^2)$ for all $i$. Suppose you want to forecast $\theta = \...
1
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0answers
39 views

variance of filtered polynomial

Consider the following system: What is the variance of $y$, $\mathbb{E}(y^2)$ ? (EDIT: I know input signal has infinite power but will be made bandlimited by $H$. Both $H$ and $G$ are simple ...
1
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0answers
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 ...
1
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0answers
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}...
1
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0answers
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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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 ...
1
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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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0answers
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 ...
1
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0answers
189 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....
0
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0answers
43 views

What is the error rate in compressed sensing?

Let $x \in \mathbb{R}^n$ be a $k$-sparse vector. Given $A \in \mathbb{R}^{m \times n}$, we have a measurement vector $y$ given by $$y=Ax$$ Let $\hat{x}$ be defined as follows $$\hat{x}:=\arg\min_{z\...
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0answers
36 views

About the power spectrum and confidence upper limit of a time-series data

For now, I have a coupled system with 5 variables and use the Runge-Kutta method to integrate. ...
0
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1answer
39 views

How would I fit a distribution to this image noise?

I have collected some noise data from a dimly lit CMOS image sensor. The distribution of pixel values is tallied below:- I'd like to be able to simulate this sensor noise. How would I fit a ...
0
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0answers
87 views

What is the difference between Statistical Signal Processing and Estimation and Detection?

Looking at the syllabus of Statistical Signal Processing in different university I see a lot of correlation with that of Estimation and Detection? In some universities, these are seen the same. For ...
0
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1answer
117 views

Redistributing Color in a RGB Image According to a Gaussian Distribution

I haven't done this stuff in a while. If I have an image $I$ I can equalize the histogram of the image using some opencv procedure, it's already defined. Equalizing an histogram means essentially to ...
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0answers
31 views

Kalman Filter - Gaussian representation

I'm trying to understand well the kalman filter, as a result i'm having this question : Why do we represent noise with a Gaussian ? what does this really mean intuitively ?
0
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0answers
352 views

Wiener filter yielding negative MSE (and MMSE)

I implement a Wiener filter using the following code ...
0
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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 ...
0
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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 ...
-1
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1answer
32 views

Spatial diversity: symbol error probability, upper bound

I am trying to understand the calculation upper bound that is given in book. Edit 1: I added 3,44 Can someone explain to me how to come from (5.5) to (5.7) ?