# Questions tagged [statistics]

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

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84 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 ...
60 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 ...
110 views

### Block by block CCDF and PAPR analysis in MATLAB

There are few signals (OFDM-like modulation scheme with uniformly distributed data source) generated by my script. I need to compare scheme performance in sense of CCDF (Complementary Cumulative ...
12 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 ...
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 ...
66 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 ...
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### 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 ...
37 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 ...
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, ...
63 views

### Derivation of Circular Mean Square Error

I would like to understand how Eq. (36) in  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....
40 views

### Cepstrum of white gaussian noise

What are the statistics of the cepstrum of gaussian white noise? \begin{align}\newcommand{\Nfft}{ {N_{\mathrm{FFT}} }}\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT} x_i &\sim \...
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### 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 ...
205 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. ...
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### 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 ...
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### What does Allan variance really means? [duplicate]

Let a sensor (e.g. accelerometer) with a combination of white gaussian noise and random walk noise. The loglog plot that is usually shown as function of a time parameter, affine decreasing for a ...
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### How to Average Complex Responses (and Justification)?

I am developing software that calculates the response of a system by comparing the FFT of input and output signals. The input and output signals are divided into windows and, for each window, the ...
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 ...
63 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\...