Questions tagged [statistics]
Statistics is the study of the collection, organization, analysis, and interpretation of data.
218
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What is the difference between the general white process and the white process of order 𝑝?
Antoni uses the following definition of white process of order $p$:
a process whose all cumulants up to order p are such that
$$\text{Cum}\left[X(t),X(t-\tau_1)\cdots,X(t-\tau_{r-1})\right]=C_{rX}\...
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Is there a quadratic version of exponential smoothing?
I have a time series - let's say I'm given one new sample (a real value) every second.
I could take a moving average of the last 50
samples or I could use exponential smoothing of the samples with a ...
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1
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79
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Sampling a pulse train with a controllable square wave
I have an issue regarding a sampling process of a pulse train in an image sensor based on events. Basically, these are a family of image sensors in which each pixel outputs a train of pulses, and the ...
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What is the relation between the 1/f spectral noise density and the Allan deviation noise floor? (I found a value of $\frac{5}{3}$)
I have some noise density that consists of 1/f noise and white noise like so:
I then select an arbitrary sampling frequency $f_S$ and data length $n$ and compute a time domain noise data vector like ...
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155
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1/f noise: Why does the Allan Deviation remain constant, while standard error of mean keeps decreasing for long averages?
It is a rather well-known fact, that measurement precision is limited by the 1/f noise of a signal [1]. One way to show this in a concise fashion, is to plot the Allan deviation of the signal. For ...
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1
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39
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Comparing methods of blind source separation
I am currently working on blind source separation using sparse hypotheses and convolutive mixtures. For my project, I have compared three different methods and calculated the Signal-to-Distortion ...
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10
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How to use HAC for Time Series Dataframes with Covariance
I have a question concerning time series.
I have a Dataframe with several Columns, each containing a time series.
I need a Covariance Matrix of the different columns.
However, my columns are ...
2
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1
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113
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How to find the variance of a noise signal distorting an ADC measurement
Say we have a 12-bit ADC measuring a signal with a voltage range of 0-10V, but the signal is corrupted by uniformly distributed 3-bit white noise. What's the correct way to get the variance of the ...
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1
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45
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Expectation and autocorrelation for modulated sinusoid
Given
$$ Y(t) = A X(t) \cos(\omega t + \phi) $$
with $X(t)$ is zero-mean WSS (wide-sense stationary) process, $\phi$ ~ Unif$(0,2\pi)$. Suppose $X(t)$ and $\phi$ are independent random variables. I ...
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64
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Why is the total noise variance less than the sum of individual noise variances?
I have three random variables:
$Y$: my data
$Y_n$: my data corrupted by additive white Gaussian noise (AWGN)
$Y_{nc}$: my noisy data corrupted by a non-linear transformation $\mathcal{C}$.
I have ...
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43
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Variance of Value Expressed as Number of Changing Bits
I consider values physical measurements, expressed as variables of type int16, uint32, float ...
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56
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How to figure out or estimate the level of noise in a given data distribution
I have been given a data distribution which was synthetically generated by geostatistical methods such as variogram analysis. Without having the source of the technique which generated the data, is ...
4
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1
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71
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Calculate magnitude of the gradient using higher order statistics
I am making a model for detecting blurred part of an image. I'm using features described in the paper Blurred Image Region Detection And Segmentation by Hyukzae Lee and Changick Kim, and I have a ...
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1
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459
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How to Find Median Frequency of Binned Signal (FFT)?
I want to find the median frequency from the FFT result. All I have is binned data I got from FFT (An array).
I'm doing this calculation in C, so I don't have access to the statistic tools from MATLAB ...
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1
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446
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Choice of relationship between n_fft and window_length in STFT
Not a veteran in Signal Processing, it would be extremely appreciated to help me understand the idea/heuristic behinde the idea in STFT that
$$\text{nfft} \ge \text{window length}$$
At least from a ...
1
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1
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103
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Why is a random process strictly stationary when its joint Probability density function is time invariant?
I don't understand what stationarity of random process mean.
I know they're statistical properties that are time invariant but I don't have intuition for it and I don't get what that has to do with ...
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What is the difference between Yule Walker and Modified Yule Walker Equation that used in Stochastic Signal Modeling?
Our Professor couldn't explain the clear difference between the Yule Walker equation and the Modified version of it that is used in Stochastic models. Please explain both the equations and why we ...
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2
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167
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Why is Autocorrelation between a Zero-mean Random process and a finite deterministic sequence zero?
The Solution is given above:
The Question is, how did the $\mathbb{E}{[x(k)f(l)]}$ and $\mathbb{E}{[x(l)f(k)]}$ become zero? is there some rule that correlation between Random Process and ...
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0
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57
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Understanding Quantile-Quantile Plot of my Signal
I have computed the Q-Q plot of my dataset, which is a recording from a brain signal, and it shows a curious left and right skewness displacement, and I was wondering if this is any other distribution ...
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1
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123
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What is the sum $\sum_{m} e^{i (U_m k + \beta_m)} $ when $U$ and $\beta$ follow different distributions
I have the following function.
$$ x(k) = \sum_{m} e^{i (U_m k + \beta_m)} $$
$i = \sqrt{-1}$
Here, $U_m$ are samples drawn from a Gaussian random distribution.
$$ U_m \sim \mathcal{N}(\mu, \sigma) $$ ...
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1
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109
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Imitate noise audio file with math function
Is it possible to reverse engineer a short white noise audio file and imitate it with a function instead?
The file doesn't contain pure white noise, there has been EQ applied to it, also some ...
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Stationarity Test on Dataset
I have a nice and clean noise signal sampled at a fixed rate for several hours. When I calculate the PSD I see it's pure flicker noise. But I don't know much about the process.
I've seen some ...
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1
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Order statistics: always applicable tool in wireless communication?
I have seen few papers where generalized order statistics is used to obtain statistics of the instantaneous SNR.
"Performance analysis of monostatic multi-tag backscatter systems with general ...
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1
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339
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Autocorrelation and the dot product of complex signals
I have a question for the signal processing community.
When trying to calculate the autocorrelation of an array containing complex data, could the result be purely imaginary, and is there any ...
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1
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56
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How to interpret arg min in the the following equation?
I am studying the following equation:
$$\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)...
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1
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42
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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 ...
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0
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105
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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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45
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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 ...
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1
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91
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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 ...
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0
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58
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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:...
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2
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879
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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?
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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 ...
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100
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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} = \...
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64
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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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53
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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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98
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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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73
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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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39
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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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0
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81
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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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1
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48
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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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95
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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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88
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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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1k
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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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895
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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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53
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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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1k
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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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426
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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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483
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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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1
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190
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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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174
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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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