# 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 ...
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, "...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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)...
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 ...
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 ...
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, ...
28 views

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 ...
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 ...
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-...
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 ...
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, ...
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 \...
89 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....
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 ...