Questions tagged [statistics]

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

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36 views

Imitate noise audio file with math function

Is it possible to reverse engineer a short white noise audio file and imitate it with a function instead? The file doesn't contain pure white noise, there has been EQ applied to it, also some ...
1 vote
0 answers
20 views

Stationarity Test on Dataset

I have a nice and clean noise signal sampled at a fixed rate for several hours. When I calculate the PSD I see it's pure flicker noise. But I don't know much about the process. I've seen some ...
0 votes
1 answer
25 views

Order statistics: always applicable tool in wireless communication?

I have seen few papers where generalized order statistics is used to obtain statistics of the instantaneous SNR. "Performance analysis of monostatic multi-tag backscatter systems with general ...
0 votes
1 answer
52 views

Autocorrelation and the dot product of complex signals

I have a question for the signal processing community. When trying to calculate the autocorrelation of an array containing complex data, could the result be purely imaginary, and is there any ...
0 votes
0 answers
12 views

Get shape of a recurring pulse event in my plant video signal

I'm studying plants - specifically how the color of their leaves change throughout a day. I have a camera pointing at a leaf which takes a picture every 47 minutes and calculates the average green ...
-1 votes
1 answer
217 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 ...
0 votes
1 answer
49 views

How to interpret arg min in the the following equation?

I am studying the following equation: $$\hat{s}_m(n) = \arg \min_{s_m(n)\in A_s}\left| \frac{\psi_m^H}{||\psi_m^H||^2}y_m(n)-s_m(n)\right|^2\tag{1}$$ here $A_s$ is 1x$N$ vector of QPSK symbols, $s_m(n)...
1 vote
1 answer
34 views

Standardizing signals from the same experiment setup with different recording tools

I've been looking to merge two datasets I have, that capture instances of the same phenomenon using two different recording tools. Both are multichannel electrical signals, but the recording tools ...
2 votes
1 answer
2k views

Integral over power spectral density

The Wikipedia entry on Spectral Density (PSD) has one confusing line: Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical ...
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0 answers
27 views

Affine transformation on circularly symmetric Gaussian distribution

Assume the complex random vector $\mathbf{y} \in \mathbb{C}^N$ is circularly symmetric distributed i.e. $\mathbf{y} \sim \mathcal{CN}(\mathbf{0},\mathbf{R})$ $$ p_{\mathbf{y}}(\mathbf{y})=\pi^{-N}\...
1 vote
0 answers
19 views

Mann-Kendall Trend Test

I'm using the pyMannKendall package in Python to detect the presence of slope of any given waveform. More details of the package here: https://github.com/mmhs013/pyMannKendall I'm not exactly able to ...
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25 views

Particle Filter estimation: sinusoidal signal

I am designing a particle filter for the extraction of a sinusoidal wave with known frequency and sampling frequency from Gaussian noised biased measurements ($y=x+\text{bias}+\text{Noise}$) My state ...
1 vote
1 answer
104 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,~~~~~~~~~~...
0 votes
1 answer
96 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 $...
0 votes
1 answer
96 views

Generalized Likelihood Ratio test for correlated data

Consider a sequence of random variables $\overline{z} = \{z(k-M+1), ..., z(k)\}$, with probability density depending upon a scalar parameter $\theta$. It is intended to decide between two hypotheses ...
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0 answers
40 views

Help with creating/drawing the PDF of signals X and Y

Given is an analogue source $x$ equally distributed in the interval $[-1;+2]$. By means of a mapping, the signal $Y$ is calculated according to $Y = (X - 1)^3$ is generated. Sketch the $PDF$ of the ...
0 votes
1 answer
43 views

How to interpret Allen Deviation with increasing negative slope

I was calculating the Allan deviation (utilizing the Python module allantools.adev, which relies on eq. (6) in https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50505). The expected behavior is a ...
7 votes
1 answer
105 views

Concept About Estimated Standard Deviation

I am looking for the concept about how to estimate standard deviation. Actually I'm not sure how can I get a concept the estimate standard deviation ? If you know the concept, then would you let me ...
1 vote
0 answers
46 views

Linearity of the system with Pearson correlation sliding window

I have a sampling system that consists of linear and non-linear components(analog filters, ADC, CPU, and so on). I made some HW changes and I want to verify that the linearity was preserved. My method:...
6 votes
2 answers
196 views

Minimum Mean Square Estimator - Equivalent Expressions to Minimize

Given $ M \in \mathbb{R}^{N \times N} $ which is a Positive Definite Matrix. Let $ \hat{x} $ the MMSE of $ x $ given $ z $, namely $ \hat{x} = \mathbb{E} \left[ x \mid z \right] $. Prove the ...
4 votes
1 answer
3k 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 ...
0 votes
0 answers
25 views

How to handle skewness and kurtosis parameters of missing data?

I'm working on acoustic signal classifier. Most signals are characterized by having two echoes (peaks). Each echo can be described by maximum value, duration, skewness and kurtosis. Thus each signal ...
13 votes
7 answers
8k views

Good book or reference to learn Kalman Filter

I am totally new to the Kalman filter. I've had some basic courses on conditional probability and linear algebra. Can someone suggest a good book or any resource on the web which can help me can ...
0 votes
2 answers
297 views

Quantization error standard deviation

Here I found that "pure" quantization error standard deviation of the signal is $1/\sqrt{12}$ of LSB. Where does it come from?
5 votes
1 answer
625 views

Is Allan variance still relevant?

I've been working with Allan variance for a while and I'm not really super excited about is purpose. I understand that noise time recordings, if they include flicker noise, diverge in time. In other ...
4 votes
1 answer
70 views

Adding Variance \ Weights Information When Solving a Basis Pursuit Denoising Problem (BPDN)

Having a "measured" vector $\mathbf{y}$ with its statistics (counts or variance per element), one can use weighted least squares approach to solve the linear system $$\mathbf{A}\mathbf{x} = \...
0 votes
0 answers
15 views

How to use numpy covariance result to get a correction factor and make my second signal to exactly overlap on my first signal?

covariance = np.cov(y1_interp, y2_interp)[0][1] print('covariance is', covariance) covariance is 0.00010861874695023591 This number shows how different my signal 2 ...
0 votes
0 answers
72 views

Dividing a data set into segments with consistent inner behavior, using segmentation algorithms and metrics for consistency

Context of the problem: I have signal data which was recorded in a software system and which shows the runtime of multiple processes over time. In total there are more than 900 processes each having ...
2 votes
0 answers
43 views

Estimating shot noise - what's the origin?

If I have some photon detector, say a CCD, how do I estimate the error introduced by shot noise correctly? Typically, sources found on the internet say that the shot noise is the square root of the ...
1 vote
1 answer
97 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 votes
1 answer
31 views

Infinity values in statistical analysis of minute frequency data

I'm trying to extract statistical features from power spectral density values in Python. My data is actigraphy data with sampling rate 1/60 Hz (once per minute). This is a sample from my data, "...
0 votes
1 answer
45 views

Is "Introduction to Statistical Signal Processing" by RM Gray good for starting?

I am working on noise processes in electronic devices for my studies, by now Ive been doing a fairly large amount of processing of time measurements, like calculate PSD, estimate thermal, flicker ...
15 votes
3 answers
2k views

What Does It Mean Exactly When Two Parts of a Signal Are Correlated?

I stumble quite often upon the notion that two or more parts of a signal are correlated to describe semi-formally that they belong together. For example in image processing, two pixels on an edge ...
1 vote
1 answer
52 views

Reduce signal length while maintaining properties?

I am new to DSP. So I have a noisy signal with some high-frequency components. I was able to characterize the statistical properties of this signal through a gaussian distribution. My aim is to run a ...
0 votes
1 answer
37 views

Is RMS or MEAN appropriate for a DC current signal?

I've extracted SCADA data recording (every 2 seconds) the DC current applied from a DC power supply (Sorenson SGA) during a steady state (current control mode) electrolysis trial. To report the ...
0 votes
0 answers
55 views

Is sum of squares of normally distributed Random variables follow Chi square distribution?

Actually standardized variable z of x(which has a normal distrbution) is (x - E(x))/squareroot(E(x-E(x)) ^ 2) In chi-square distribution we have that sum of squares of unit normal distribution ...
1 vote
1 answer
37 views

Can Goodness-of-fit increase while noise also increases?

I saw a tweet with a good slide. It has a Goodness-of-fit curve that goes up with Model Complexity. There is a Generalizability curve. Noise is cited as the difference between the GOF and ...
1 vote
0 answers
67 views

Fisher Information Matrix for sinusoidal signal under multiplicative noise

Consider observations ($y$) of a sinusoidal wave with multiplicative noise ($v$) where we are estimating unknown frequency ($\omega$) and unknown initial phase ($\theta$). We can write this system ...
1 vote
1 answer
63 views

RF-Chain Signal Delay for Sensor Switching

Lets have a RF-chain as above with system bandwith from HP corner to the green line say 1 MHz. The signal accumulates delay as it passes through this analog chain, and due to it being non-liner filter ...
0 votes
1 answer
421 views

Calculating total power for the signal

In my previous question I asked about calculating a single number as "Spectral Density" feature from signal data. We concluded that it is really a total power and article (link) authors ...
0 votes
0 answers
368 views

Trying to implement matlab pwelch function in python using scipy welch

I am trying to port the statistics toolbox function pwelch from matlab into python, but when I am trying to implement it using scipy.signals.welch, it does not return the same results as it does in ...
0 votes
2 answers
67 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?
1 vote
0 answers
50 views

Short Time Fourier Transform has different frequencies than Fourier Transform?

The reason we do the STFT is so that we can analyse for short segments of time how much of the components in the frequencies of the FT are present. However, it may be possible that completely ...
6 votes
1 answer
5k views

How can I calculate the Expectation for a particular known vector?

Let us say I have a row vector $X = [x_1, x_2, x_3, \ldots, x_n]$ and another row vector $Y = [y_1, y_2, y_3, \ldots, y_n]$. I want to check whether the two vectors are statistically independent or ...
6 votes
2 answers
336 views

How to Calculate Local Spatial Variance of an Image?

For those who work often on image processing, I'm facing an algorithm of Non-Uniformity Correction (NUC) that requires the calculation of a parameter called "Local Spatial Variance". I can't ...
0 votes
0 answers
111 views

Choose the right Sigma for Gaussian filter

I have the following problem: I have a time series with counted data. I now want to smooth it using a Gaussian low-pass filter. Is there a method to determine the sigma value? The window should have a ...
2 votes
1 answer
211 views

Having problems with understanding the meaning of PSD for colored Gaussian noise

After reading two articles on signal processing stack exchange: On coloured Gaussian noise How the white and colored noise differ in time domain I do understand that variance do not change over ...
2 votes
2 answers
2k views

How to transform data to uniform distribution (uniform percentiles)?

Given the list of data points (normalized in [0,1] range), I plot the histogram of values and compute percentiles (shown as x ticks). How to find a transformation of data values so the histogram is ...
6 votes
1 answer
809 views

Subsample Time Delay Estimation

Often we need to estimate the time difference of arrival between two signals to find the location of a target. Many algorithms gives the time delay corresponding to a sample number or time delay is a ...
1 vote
3 answers
397 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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