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Questions tagged [statistics]

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

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Kalman Filter: handling large covariance matrices with principal-component-like structures

I understand that the estimation of the covariance matrices are the important part of the Kalman filter. However in my use case my covariance matrices are really big but with a pretty neat factor ...
Matt Frank's user avatar
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0 answers
17 views

Estimating IMU biases without using any external aid

Assuming that Inertial Measurement Unit (IMU) contains accelerometer and gyroscope, I want to estimate the bias in each of the sensors. We know that accelerometer and gyroscope have biases which ...
user146290's user avatar
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1 answer
32 views

Frequency decomposition of forecast error variance

I think my question concerns statistical signal processing. I was referred to this site by a user at Cross Validated. I want to do a frequency-domain decomposition of generalized forecast error ...
Pavel Filip's user avatar
0 votes
1 answer
56 views

Determine if measured gaussian noise have constant mean

lets say I am measuring ($z$) Gaussian noise with known variance sigma in each step, i.e. $z_k = v_k$, where $v_k$ is Gaussian distribution with known variance $\sigma_k$ (changing with each step) ...
Jakub's user avatar
  • 3
1 vote
0 answers
51 views

Statistical technique for distinguishing between artefacts and no artefacts [closed]

I would like to know how to create an algorithm from the table below in order to distinguish between data that has artefacts and data that does not. I'm trying to leverage video attributes like ...
Coder's user avatar
  • 11
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64 views

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}\...
Gideon Genadi Kogan's user avatar
1 vote
1 answer
116 views

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 ...
Peter Balch's user avatar
0 votes
1 answer
110 views

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 ...
Sergi's user avatar
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3 votes
1 answer
151 views

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 ...
tobalt's user avatar
  • 468
3 votes
1 answer
293 views

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 ...
tobalt's user avatar
  • 468
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1 answer
52 views

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 ...
BLOBA fitz's user avatar
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0 answers
14 views

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 ...
Timon Gaman's user avatar
2 votes
1 answer
131 views

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 ...
Mikayla Eckel Cifrese's user avatar
1 vote
1 answer
55 views

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 ...
XXX1010's user avatar
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1 vote
1 answer
80 views

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 ...
graille's user avatar
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1 vote
0 answers
45 views

Variance of Value Expressed as Number of Changing Bits

I consider values physical measurements, expressed as variables of type int16, uint32, float ...
Yair M's user avatar
  • 305
1 vote
1 answer
91 views

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 ...
2023_resolution's user avatar
4 votes
1 answer
71 views

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 ...
Glitterfrost's user avatar
1 vote
1 answer
687 views

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 ...
spinmaster's user avatar
2 votes
1 answer
711 views

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 ...
LambdaDelta34's user avatar
1 vote
1 answer
122 views

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 ...
mahmoud esmail's user avatar
0 votes
0 answers
158 views

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 ...
Kuchi Yashwanth's user avatar
1 vote
2 answers
233 views

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 ...
Kuchi Yashwanth's user avatar
1 vote
0 answers
61 views

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 ...
GGChe's user avatar
  • 153
0 votes
1 answer
124 views

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. $$ U_m \sim \mathcal{N}(\mu, \sigma) $$ ...
CfourPiO's user avatar
  • 107
1 vote
1 answer
127 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 ...
pepperdreamteam's user avatar
1 vote
0 answers
33 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 ...
Ralph's user avatar
  • 81
0 votes
1 answer
44 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 ...
chaaru's user avatar
  • 37
0 votes
1 answer
509 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 ...
Vatatia's user avatar
  • 41
0 votes
1 answer
60 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)...
chaaru's user avatar
  • 37
1 vote
1 answer
45 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 ...
marpuech's user avatar
1 vote
0 answers
119 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 ...
EnigmAI's user avatar
  • 111
0 votes
0 answers
45 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 ...
Caniko's user avatar
  • 1
0 votes
1 answer
105 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 ...
Sandro Camenzind's user avatar
1 vote
0 answers
60 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:...
Michael Shevelin's user avatar
0 votes
2 answers
1k 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?
Curious's user avatar
  • 355
6 votes
1 answer
2k 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 ...
Ralph's user avatar
  • 81
4 votes
1 answer
104 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} = \...
bla's user avatar
  • 588
2 votes
0 answers
68 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 ...
hintze's user avatar
  • 121
0 votes
1 answer
60 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, "...
qalis's user avatar
  • 111
1 vote
1 answer
125 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 ...
Ralph's user avatar
  • 81
1 vote
1 answer
86 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 ...
user244717's user avatar
0 votes
1 answer
40 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 ...
J Herron's user avatar
0 votes
0 answers
86 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 ...
John Siddarth's user avatar
1 vote
1 answer
56 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 ...
bliswell's user avatar
1 vote
0 answers
110 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 ...
Ahwaq's user avatar
  • 11
1 vote
1 answer
97 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 ...
BandW's user avatar
  • 105
0 votes
1 answer
2k 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 ...
qalis's user avatar
  • 111
1 vote
0 answers
1k 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 ...
Peadar O Donnell's user avatar
1 vote
0 answers
54 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 ...
Rahul Deora's user avatar

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