Questions tagged [statistics]

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

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20 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 ...
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1answer
23 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, "...
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42 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 ...
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1answer
35 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 ...
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1answer
36 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 ...
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42 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 ...
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19 views

Determination of Variance from Symbol Error Probability Equation

For a M-ary QAM receiver, the symbol with AWGN noise is received and detected with Maximum–Likelihood (ML) Decision algorithm. The symbol error probability (SEP)is approximated as : here, Eb is the ...
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17 views

How can we interpret Spatial Cross Correlation between two images in case of compressed sensing based reconstruction of images?

I am reconstructing images using compressed sensing. The images are used from sipi database. One particular image, named Female Bell Lab, which is giving better result with high PSNR around 42 dB and ...
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1answer
31 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 ...
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59 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 ...
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15 views

What are some good references that define images from a statistical point of view?

I know that images can be studied and understood as 2 dimensional signals. However, I hope you can point me towards references that define and present images rigorously in terms of realisations of a ...
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1answer
55 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 ...
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1answer
67 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 ...
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51 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 ...
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18 views

Unable to interpret hypothesis testing whetehr a signal is periodic or not

The meaning of P value is probability which should be number between 0 (the event never occurs) and 1 (the event occurs always). significance testing for periodicity using Matlab gives a documentation ...
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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 ...
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2answers
79 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 ...
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21 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 ...
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13 views

Calculate ACF in C++?

I would like to manually reproduce the method that authors of an article used in their research (DOI: 10.1038/s41598-017-02750-9 (Page 8. top)). It is mentioned as "ACF", so I wrote ...
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1answer
99 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 ...
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1answer
27 views

What's the difference between nonstationary and time varying?

I am confused by the following statement from the paper Beamforming: A Versatile Approach to Spatial Filtering by Barry D. and Kevin M.: There are two basic adaptive approach: 1) block adaption ..., 2)...
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69 views

What is the physical significance of statistical quantities like mean, variance, skewness and kurtosis of a digital signal?

I understood the mathematical meanings of the mean, variance, skewness and kurtosis. But when we calculate these quantities for a signal (say a digital audio signal), what physical meaning do they ...
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1answer
36 views

Effectively extracting “real” data from a noisy dataset

This question was originally posed to Math SE. It was suggested that DSP SE would be more suitable. Background & Motivation: I have three lists of timestamps (UNIX timestamps, plus a subsecond ...
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22 views

When is Markov a Martingale

I have two questions and I am very confused about the concepts Can a Markov process of order one also be a a Martingale? Is any Markov process of order one also a Martingale? For 1. I would say yes, ...
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28 views

Generating data with given Auto and Cross Correlations

I have two discrete vectors $\mathbf{x}_1$ and $\mathbf{x}_2$, and I'm trying to generate more data $\mathbf{f}_1$ and $\mathbf{f}_2$ that has some basics properties of $\mathbf{x}_1$ and $\mathbf{x}...
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2answers
50 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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12 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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1answer
58 views

What Are Intuitive Explanations for Shrinkage in the Context of Image Denoising?

I have occasionally come upon the term "shrinkage", mostly in the context of denoising methods. My rough understanding is that it refers to the part where the real distribution might not be ...
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28 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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13 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
149 views

What will be the distribution of a given signal

Suppose I have a signal $$ \mathbf{s} \sim C \mathcal{N}\left(\mathbf{0}, \sigma^{2} \mathbf{I}_{N_{}}\right) $$ The signal going through a channel : $$ {\mathbf{r}}_{}=\mathbf{s}+{\delta \mathbf{n}} ...
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1answer
44 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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3answers
231 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
74 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
26 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
73 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
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
79 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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1answer
89 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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56 views

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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29 views

About convergence of KL divergence: if the two probability distributions are type, does the law of large number work?

If I pick $N$ samples from $P_X$ and $P_Y$, they are two independent discrete distributions. $X_1,X_2,\ldots,X_N$ are drawn i.i.d from $P_X$, and $Y_1,\ldots,Y_N$ are drawn i.i.d from $P_Y$. I got $...
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1answer
174 views

How to get info (mean,std) out of normplot in matlab?

Lets say we have the following data and then we have a normplot: load census; h=normplot(cdate); [mean std]=normfit(cdate); I know i can get the mean(1890) and ...
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1answer
291 views

Sum of correlated exponential random variables

How do we find PDF of sum of correlated exponential random variables. I know for independent random variables. But how to find it for correlated exponential random variables.
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2answers
77 views

Lightweight test for bimodal distributions?

Here, and in the stats stackexchange, seem to be answers that reference tests for bimodal distributions that involve iterative binning or iterative curve fitting methods. However "eyeballing" a plot ...
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1answer
66 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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1answer
336 views

The expectation in power spectral density

I'm a bit confused with the definition of the power spectral density (PSD). From Wiki https://en.wikipedia.org/wiki/Spectral_density , I found the definition is: $$ S_{xx}(\omega) = \lim_{T\...
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33 views

CWT coefficients as features for ML algorithms

I use CWT coefficients as features in ML algorithms and then I did the feature selection using the chi-square test but recently I figured out that the chi-square test can only be applied for ...
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24 views

Finding the error in the total integrated intensity of a fitted 2D Gaussian

I have been trying to fit signals to a 2D Gaussian function, and while I have bene able to use sciKit-image's curve_fit function to find the covariance matrix for ...
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20 views

ICA School Project

I have been stuck on my school project that consists of independent component analysis. My code will run, but only 50-60% of the time it unmixes the signals. Another problem I have is the amplitudes ...
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1answer
142 views

Autocorrelation for Stationary Signals

I'm having trouble grasping the autocorrelation function for stationary signals, both strict stationary and WSS. First for strict sense, we have $$\forall(\tau,t_1, \ldots, t_n) \in \mathbb{R} \land ...