Questions tagged [signal-processing]

Numerical analysis of a digitized signal

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Unscented Kalman filter-negative covariance matrix

I have recently started working on the unscented Kalman filter. I coded the numerically stable version (i.e., square root Kalman filter) and used MATLAB for implementing. In the final update step, ...
6
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0answers
92 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 ...
5
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0answers
146 views

How to improve estimation of a deconvolved density

I have the following problem: Y = X + e with Y = Total reaction time (noisy signal) X = selection time (signal) e = discrimination time (noise) I am interestend in the distribution for X and ...
5
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0answers
2k views

What is the best way to compare fluctuations of two signals?

I have some data acquired by an acoustic sensor with 1 Hz sampling rate. Due to some inevitable issues, I have some noise in my signal, saying 10% pollution. I'm looking for a reliable method for ...
4
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0answers
610 views

Sensor data cleaning

Underneath is a picture of a sensor measuring the fill rate of a container on an hourly basis. It goes up to 100% and is then emptied. There is some natural deviation of the sensor due to temperature ...
3
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0answers
35 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) ...
3
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1answer
166 views

Formulas for higher order cumulants

I want to calculate higher-order joint cumulants for 2 variables. I calculated the higher order single-variable and bivariate moments numerically. Now I need to combine them into cumulants (upto the ...
3
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0answers
189 views

How can I get the cumulant expression from the recursive relation between cumulant and moment?

I am reading some paper about high-order statistics https://link.springer.com/article/10.1007%2Fs11004-009-9258-9?LI=true. The paper gives two recursive expressions relating the multivariate cumulants ...
3
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0answers
96 views

2D Sensor data alignment by correlation

I have an analog Video Signal in Octave (=Matlab). It is sampled by 14Msample/s. By autocorrelation I have found the line frequency of 15,625KHz. I have 896 samples per Line. But when I transfrom now ...
3
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0answers
120 views

Survival (Kaplan Meier) of signal transmission that can both fail and recover

I'm investigating the failure to transmit of a number of signals in time. In my data I often see signals transmitting for quite a long time, but after some time they gradually start failing but still ...
3
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0answers
157 views

On the choice of activation functions for neural networks (coming from signal processing)

As far as I understood the gist of this paper, learning a representation that is invariant under some one parameter group $\{U_t\}$ (e.g. 1D translations) can be accomplished by letting the ...
3
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0answers
53 views

Signal processing techniques for unevenly spaced and repeated measures series

I am considering using signal processing techniques to find the minimum on a noisy 1D response line. More specifically I have a simulation that requires one parameter, but also includes randomness, ...
3
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0answers
437 views

Error Bars for Peaks in Noisy Data

I'm doing an experiment where peaks in amplitude $A$ (the dependent variable) are expected as one varies the frequency $f$ (the independent variable). Based on our theoretical model, Away from the ...
3
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0answers
170 views

A best measure for speaker recognition

I have a set $E_{1}$, with a finite cardinality $n$ of rectangular matrices which contains the useful MFCC coefficients generated from $n$ speech signals. Similary I have a set $E_{2}$ of same ...
2
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0answers
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 ...
2
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0answers
45 views

Finding exponential decay in noisy vibration signal

I have to analyse vibrational signals for which the general assumption is that there is one dominant excitation and an exponential decay in amplitude thereafter. I have created smoothened envelopes ...
2
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0answers
36 views

Signal Decomposition

I have two time dependent signal sources X & Y. Both can be modeled as having a linear combination of time dependent individual components and common components; so X(t)=a(t)+C(t)+noise, Y(t)=b(t)+...
2
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0answers
130 views

Detecting specific points in (noisy) dataset

In my recent work I've came across a problem where I need to find certain points in quickly oscillating data. Let's work with syntethic data instead of real measurements and ignore the noise for the ...
2
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1answer
49 views

Verifying Time Warp

Time warp has been widely assumed in domain of speech processing. If $Xw(t)$ represents a time warped version of $X(t)$, then $Xw(t) = X(t-w(t))$ where $w(t)$ is an arbitrary function with a banded ...
2
votes
1answer
302 views

What is the differennce between invariance to translation, covariance to translation and equivariance to translation?

I get stuck at understanding the difference between invariance to translation, covariance to translation and equivariance to translation in the context of of convolutional neural network. What does ...
2
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0answers
60 views

Continuous entropy comparison

I have a continuos time signal (speech signal) and I will add noise to it at different SNRs. I want to compare the entropy or the original signal (clean speech) with the noisy ones. The idea is to ...
2
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1answer
122 views

How to detect the change points in a signal?

I have a signal that I obtained by computing the pixel-based-sum of the difference between consecutive image frames in a video. Basically, I want to detect whenever there is a lack of continuity ...
2
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0answers
94 views

Detect different fonts of audio from a single audio source

My code uses Google Voice API, to detect what one person said. For example, if I say one, two, three on my microphone the Google's API returns to me ...
2
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0answers
41 views

Can I replace traditional DSP with statistical methods

I work a lot with noisy time traces with usually 2.5e6 data points and sampling frequency ~ MHz. I usually apply some "traditional" digital signal processing utilities like low/high-pass filters to ...
2
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0answers
392 views

Time Series Shocks with Exponential Decay

Imagine a piano key played in an auditorium: The amplitude of the sound wave is perhaps highest in the first milliseconds, then slowly decays to zero if no other notes are played. If other notes are ...
2
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0answers
171 views

Lomb-Scargle and evenly spaced data

Currently I am implementing computer program for calculating periodograms using Lomb-Scargle method. I have implemented two methods, one using double precision arithmetics (~16 significant decimal ...
2
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0answers
262 views

Clustering and Feature Selection For Audio Data

I'm very new to stats and I'm at a loss as to where to start with this problem. I'm not sure what tools or methods to use to extract meaningful answers from my data. I'll try and describe the problem ...
2
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0answers
115 views

Pattern finding approaches

I'm looking for patterns in a signal. I had used successfully a cross-correlation approach. However, I found some references to Gibbs sampling approaches for finding patterns. My question is: Are ...
2
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0answers
646 views

Defining norm of a matrix of MFCC coefficients

Scenario Construction: I have a MFCC generator block which gets the speech samples from the user and generates a rectangular matrix say $A$ of the order $m \times n$, whose elements are the Cesptral ...
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0answers
24 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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0answers
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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0answers
33 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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0answers
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 ...
1
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0answers
26 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 ...
1
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0answers
33 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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0answers
19 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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0answers
32 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: ...
1
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1answer
62 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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0answers
65 views

What is the laplace transform of the below given PDF?

Really am interesting to know more about statistical properties of the following PDF , of the Random variable $z$: $$F(\sigma,\mu,z)= \frac{(z-\sigma )^2 \exp \left(-\frac{(z-\sigma )^2 \sqrt{\left(...
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0answers
26 views

How to determine causal relationship between two temporal signals?

I have two noisy temporal 1D signals and knowledge that one drives the other, to some degree. You can see this because there are some temporary spikes in the first signal that (sometimes, if they're ...
1
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0answers
90 views

How to search for irregular signals: Fourier, DWT or k-means?

See my notebook here I want to search for irregular time signals in a data set of ~3 500 000 time signals. I can't give a clear definition of irregular signal, but it must fulfil the criteria of: not ...
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0answers
51 views

Cepstrum: quefrency scale to frequency scale

Can someone please explain to me how to convert a quefrency scale to the corresponding freqncy? For example consider this: A voice signal is measured at 50kHz sampling frequency and FFT power ...
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0answers
16 views

An Interesting Model with Unknown Orthogonal Design Matrix

Consider a linear mixed model, $$\mathbf{y}_{ij}=\mathbf{\Gamma}\mathbf{\mu}+\mathbf{z}_i+\mathbf{e}_{ij}, ~~ ~~i=1,\ldots,m,~~j=1,\ldots,n_i, $$ where $\mathbf{y}_{ij}$ are $k\times 1$ observation ...
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0answers
41 views

Variances add, and therefore subtract?

Variances add, so va + vb = vc. If I know what va and vc are, can I estimate vb by vb = vc - va ? More specifically, I have a noisy statistical time series which consists of the pure signal plus ...
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0answers
35 views

Find roots of regression function

Physical problem: Signal data comes from several sensors (e.g. 4) and there is empirical knowledge, that data of one of them (e.g. "productivity") depends on other data. Signals of other sensors could ...
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0answers
41 views

What is matching pursuit algorithm?

I would like to know What is matching pursuit algorithm? I did search via different sources but no understandable explanation is available! Can anyone help with this, please?
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0answers
19 views

Is there a concept of weakly periodic in stats? If so, what is it called?

Ok, say we have a signal that reoccurs within every T+x time where T is a constant and x is a random number small in size compared to T. We know that a function is actually periodic if F(x) = F(x+T), ...
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0answers
102 views

Comparing PCA representations between low-pass and high-pass filtered time-series data

I am currently trying to reduce the number of variables I input into a vector autoregressive (VAR) model. For those that don't already know, VAR models are used on time-series data. My primary concern ...
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0answers
107 views

covariance matrix vs correlation matrix for multiple signal analysis

I'm dealing with a set of +100 input signals, and one output. I want to explore how each of the signals affects the output. Should I focus on covariance matrix, or correlation matrix, and why? I ...
1
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1answer
67 views

Is (1 - Coherence) a metric, at a given frequency?

I'm performing some signal analysis and was using coherence (magnitude-squared coherence) to inference signals similarity. Now, I need to extend the framework by introducing a metric. I was wondering,...