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Numerical analysis of a digitized signal

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How to Add two white random gaussian noises from different noise sources?

I have generated two different white gaussian random noises in MATLAB using two different seeds. For example: Asn1 = sqrt(noisepow1/2)* (randn(size(As))+1i*(randn(size(As)))); Asn2 = sqrt(...
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34 views

Fitting sums of Gaussian-like density functions

I acknowledge that similar question has been asked a couple years ago, yet it still seems unresolved. Ignoring the domain knowledge, the statistical problem behind is to fit a non-linear regression ...
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31 views

Fitting data to sums of squares of sinusoids

I am given some time series data $(t, y(t))$ sampled at regular intervals $t=0,s,2s,3s,\ldots,1$ for some step size $s$, obtained from a function $$ y(t) = y(t, \vec A, \vec \delta) = \sum_{i=1}^N ...
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Unable to interpret p statistics for periodicity testing of signals [duplicate]

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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33 views

Detect regularity in arrival times

I am working with series of arrival times. My typical dataset is made of 20-100 samples. I would like to detect regularity in the arrival time. By regularity, I mean that the inter-arrival times may ...
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15 views

Is it a good practice to pad signal before feature extraction?

I have a question for you - is padding, before feature extraction with VGGish, a good practice? Our padding technique is to find the longest signal (which is loaded .wav signal) and then in every ...
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29 views

Kalman gain without noise

I have the Kalman gain defined as $K_k=P_{k,k-1}H_k^TS_k^{-1}$ with $S_k=H_k P_{k,k-1}H_k^T+R_k$. Commonly, in the univariate case, this is written as $K_k=\frac{\sigma^2_{process}}{\sigma^2_{process}+...
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9 views

Choose the right Sigma for Gaussian low-pass 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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29 views

Does the convergence rate never increase of a Stationary Ergodic Random Processes under sub-sampling?

Summarize the problem Given A Stationary Random Processes (strict sense) $X_i$ I define two Stationary Ergodic Random Processes by $$ \bar{X}_n = \frac{1}{n} \sum_{i=0}^{n-1} X_i \ \ \text{and} \ \ \...
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42 views

how to make Kalman filter results equivalent to linear regression? [duplicate]

Statistics gurus, Kalman filter appears to be a powerful estimator for linear problems. I understand one can tune the performance by adjusting parameters like process noise and measurement noise. Is ...
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12 views

Generation of multiple arrays or vectors with specific correlation among it?

I shall try to elaborate my question as much as possible because I tried multiple things but I am not available to find a possible solution. Problem Statement : I have an impulse response, say a ...
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12 views

Correlation estimation by the Blackman-Tukey method

Problem statement: Assume that the spectral estimation for an unknown signal is given by the Blackman-Tukey method as follows: $$ S_x(\omega) = 5+8\cos(\omega)-6\cos(2\omega)+2\cos(3\omega).$$ Assume ...
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34 views

Finding autocorrelation coefficients given PSD values at 2 frequencies

Assuming that $S_X(w)$ denotes powers spectral density function at frequency $w$, we are given $$S_X\left(\frac{\pi}{4}\right)=10+3\sqrt{2},\quad S_X\left(\frac{\pi}{6}\right)=11+3\sqrt{3}.$$ We also ...
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18 views

Is the t-test valid for the real measurement?

I'm working with a real signal measured by a machine. I've compute the mean and standard deviation, it's nearly the same. However the Allan deviation is not good enough. I want to estimate the noise ...
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1answer
24 views

Step change detection in signal by convolving with step vector

I am facing the following problem in signal processing and I have run into a wall. I am trying to detect abrupt changes (step changes) in a constantly decreasing signal by convoluting the signal with ...
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17 views

Seeking an algorithm to turn a continues signal into binary

I had a nice project in mind, which I will probably not going to do because of a lack of time, but I had some theoretical problem I faced there, which still bother me and might be interesting for you ...
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26 views

Spectral decomposition of the DC part of the signal

The title of the question might be misleading, but it shows how clueless I am about this problem. I have a time series of some quantity $X(t)$. I can calculate autocorrelation of this quantity $Y(\tau)...
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20 views

Calculate mean and variance of a timed signal

I have a function rapresenting a signal, where x-axis are times and y-axis are signal volts. Signal seems to be sampled at 200Hz, even if for some "times" it have 199 samples and not 200 as ...
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14 views

Can I decompose a signal in interval T between symmetric and anti-symmetric signals?

I have computed many samples of a signal $y_n[t]; t\in \{-T/2, T/2\}$ for $n=1,\ldots,N_{\text{samples}}$. I want to model this with an even function $f(t;\vec{\theta}) = f(-t; \vec{\theta})$ where $\...
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36 views

Uncertainty principle in probability theory

In probability theory, there is the covariance inequality $$\operatorname{Var}(Y) \geq \frac{\operatorname{Cov}(Y,X)^{2}}{\operatorname {Var} (X)}.$$ In signal processing, there is a similar ...
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15 views

Help with time series comparisons using periodograms

I have a dataset consisting of time series signals of different lengths obtained from different groups of patients. I am trying to understand the commonalities of the time series of each group. ...
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19 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 σ1. Now we process the signal,...
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40 views

ICA: a question about the non-gaussian requirement

I'm new in the ICA processing and I'm trying to understand the non-gaussian requirement. I read that the problem is that, if the composed data is $\mathbf{x}=\mathbf{As}$ with $\mathbf{A}$ (unknown) ...
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7 views

why is the signal divided into epochs in EEG classification?

I'm new in EEG signal classification. Studying the literature on this topic, I wonder why the EEG signals are divided in epochs, so, instead of classifying the whole signal all at once, we usually ...
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16 views

CTC Speech Recognition Model giving absurd results on actual recording

I have trained a speech recognition model which uses CTCLoss and is inspired from https://www.assemblyai.com/blog/end-to-end-speech-recognition-pytorch I trained it on the Librispeech Dataset (train-...
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1answer
41 views

Signal processing: How to patch over dip in signal using R?

I am a biologist starting to use R to analyze my data. Could anybody please help me solve my problem I encountered when working in signal processing in R? Problem I have a recording of a signal in a ...
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18 views

How can I “remove” variability in my data that is due to periodic signals, such as Temperature, RH and Solar radiation?

I have a measured signal that I know is affected by some periodic signals, such as Temperature, RH and Solar radiation. Is there a way that I can "remove" their influence from my measured ...
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1answer
42 views

What is a suitable way to reveal correlation between these two signals?

I have two time-domain data signals which look like the following: I know that variations in $x$ are able to induce variations in signal $y$, and would like to be able to show that "yes, x is ...
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59 views

Are the following model assumptions on a data stream too restrictive?

Suppose that you were to model a "generic" continuous-time real-world data signal $X$ taking values in a bounded continuum $K\subset\mathbb{R}^d$ (e.g. the body temperature of a patient or ...
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28 views

What is the meaning of noise in a dataset with no dependant variable?

My understanding of noise & signal comes from the context of bias-variance tradeoff in supervised methods. But given a dataset with no dependant variable, how do you define noise? & how do you ...
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35 views

Does it make more logical sense to model the discrete FFT output as a categorical variable or a numerical variable?

I am training a time-series data classifier and some of my features are the output of CT FFT. The results are of course discrete frequencies. I understand that they are in numerical order and higher ...
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104 views

Seeking recommended literature search terms for a solution to a specific kind of data structure?

Hopefully this isn't considered too off-topic. I'm working in industry these days and came up with a solution to an analysis problem we'd been facing. I'd like to get a sense as to whether said ...
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34 views

What is the similarity and difference between signal recovery and parameter estimation?

As per inferential approach both are estimation problem. But, in signal recovery, we estimate our input signal from the measured (noisy or noise free) observations. And, in parameter estimation, we ...
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21 views

What are the parameters in signal recovery? Whether source of these parameters are the sampling property of impulse response?

I was reading the following book: Juditsky, Anatoli, and Arkadi Nemirovski. Statistical Inference via Convex Optimization. Vol. 69. Princeton University Press, 2020. Here, I could not visualize the ...
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46 views

Smoothing methods for unevenly sampled data

I have categorical, time-series data distributed in space. It is very noisy, but over the whole series there are big shifts in distribution - my goal is to see how these shifts progressed in space. So,...
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Encoding a time series with varying time differences as an image

There are methods to encode a time series into an 'image' i.e a matrix of scalar values. Some methods include recurrence plots, gramian angular field and markov transition field. Most methods assume ...
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1answer
74 views

ML model for Signal Decomposition [closed]

So recently I got a task which can be summarized as follows: Suppose we have 3 functions f1, f2, f3 and a certain combination of the functions gives us ...
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36 views

How to identify the frequencies of periodic peak signals in a noisy time series? (with R)

Suppose to have two time series with peak signals at different frequencies, like these two: ...
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1answer
848 views

How should I approach (in Python) to detect the change points in following time-series signal? [closed]

I want to extract different signals present in this image. To do so, I want to find the boundaries of change point at 2.429 GHz, 2.444 GHz, and so on. Note: These numbers are observed visually and ...
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64 views

Why do AR(1) times series generated by two methods look similar but have different variance estimate in Python

I come across one question when I use two ways to generate AR(1) sequences. By definition, AR(1) sequence is $x_t = \phi_1 x_{t-1} + \varepsilon_t,\quad \varepsilon_t\sim N(0, \sigma^2)$ I found ...
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1answer
98 views

Periodogram explained

If I plot a periodogram of let's say sin(20x) + 2sin(80x) and it looks like this: What does it say, i.e., how do I interpret this periodogram? How could I compute ...
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1answer
20 views

Fourier analysis to retrieve components of individual spectra

I have a basic, simple question, I am a physics student, and searching internet gives me a lot of signal processing theory but couldn't find this basic answer, which I plan to implement in my speech ...
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1answer
15 views

Different signal length for each batch

I wonder if it Is it possible to have a different signal length for each batch when training a model. Batch 1 : all signals of length 1000 Batch 2 : all signals of length 2000 Batch 3 : all signals ...
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1answer
60 views

the concatenation of bivariate iid

suppose that $X \sim N\left( {0,{\sigma ^2}{I_2}} \right)$ is a bivariate white noise, and the samples ${X_1}, \cdots ,{X_N}$ are drawn from it, if we define the new random variable $Y$ with its ...
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33 views

How to reflect more global patterns in timeseries?

I have some signal data of a robot recorded in every minute each day. e.g., ...
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45 views

How can i compute noise (1 sigma error) given a signal

I have a signal organized as an image, i.e. a matrix. Each "pixel" has an error $\sigma_{i,j}$. Simplifying, let's assume that the error is the same for all the involved "pixels". How can I compute ...
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95 views

Features for binary time-series event prediction

This question is somewhat inspired by the answer to Features for time series classification. The difference to that question is that I have a dataset with multi-dimensional time-series where I have ...
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1answer
303 views

Cholesky decomposition or alternative for negatively correlated data simulations

I want to generate some signals that have a correlation distribution around a specific pre-defined correlation value (i.e., the distribution of the values of their correlation matrix is around a ...
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1answer
42 views

AR process stationarity

For $X[n] =aX[n-1]+W[n]$ When $W[n]$ is iid. One can say that $X[n]$ is the output of $W[n]$ thrown into an LTI system. So how can it be that $X[n]$ is not necessarily WSS, if we know that a WSS ...
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28 views

Math for Gaussian noise on top of another Gaussian noise

I have worked on this project for a while and I have some results. However, I want to communicate in my paper the mathematics involved. When an image is introduced with 11 standard deviations, this ...

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