Questions tagged [signal-processing]

Numerical analysis of a digitized signal

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27 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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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 ...
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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 ...
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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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312 views

why is an MA process equivalent to a FIR filter?

John Cook claims that a FIR filter is equivalent to an MA process. But FIR filter is just a function of the previous inputs: $y_t = \phi(B)x_t$ and an MA process is a function of the previous ...
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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)+...
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110 views

Viral topics. How to describe and characterize bumps in time series of tag-activity on Meta Stack Exchange

Background There is much dissatisfaction on StackExchange. This can now be covered in over 250 questions on meta (see 1 and 2). In response to that I made a recent meta-post and supported it with the ...
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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 ...
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1answer
40 views

How to discard the first spike after auto-correlation and handle sloping auto-correlation output [closed]

Disclaimer: I am not very mathematically inclined and am mostly looking to be pointed in the right direction. I have various signals that I am putting through an auto-correlation function that uses ...
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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 ...
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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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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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114 views

Can I use a LSTM Autoencoder to compute similarity between two variable-length audio signals?

I would like to compute the similarity between audio signals of different length. One way of doing it is to train a RNN (LSTM/GRU) Autoencoder and extract the hidden layer representation - feature ...
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1answer
255 views

Intuition of the convergence of sample ACF

One of the problems in Brockwell and Davis book about time series is to show that 1) if \begin{equation} x_t = a + b t \end{equation} then the sample autocorrelation ($\hat{\rho}(h)$) converges to ...
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73 views

Benefits of ML in signal processing

There is plenty of research on ML in signal processing. The majority of it, so it seams to me, is about showing feasibility of ML-based receivers (end-to-end or individual functional blocks of). To me,...
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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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204 views

Estimation of NegEntropy

I am trying to evaluate the different ICA algorithms. To do that, one of the measure which I use, is to estimate the non-gaussianity using NegEntropy. I am trying to find a formula/function which can ...
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23 views

How to test whether event A affects the frequency at which event B occurs

I conducted an experiment in which I measured the occurrence of some event A over time. I then intervened in the system, periodically introducing event B. I hypothesise that event B affects the ...
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1answer
127 views

Terminology: Is DTW considered to be machine learning or signal processing?

The DTW Wikipedia article puts this method in the category "Machine learning algorithms". On the other hand, the famous paper "Dynamic Programming Algorithm Optimization for Spoken Word Recognition" ...
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10k views

Is it a good idea to use CNN to classify 1D signal?

I am working on the sleep stage classification. I read some research articles about this topic many of them used SVM or ensemble method. Is it a good idea to use convolutional neural network to ...
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1answer
129 views

Strange accuracy graph

I was training my NN when I found out something I CAN NOT understand. My net is a bilstmLayer and a softmaxLayer layer with 10 MaxEpochs and 150 MiniBatchSize. I want to classify 4 different type of ...
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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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76 views

How to deal with varying number of intervals and hence varying number of features dividing an audio signal while classifying these audio signals?

I've $2000$ audio signals, each divided into a number of time intervals/time frames of $50$ miliseconds (ms) and these signals have overlaps for $25$ ms. Now, the audio signals being of different time ...
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21 views

Clearing out errors from a data set

Sorry for the vagueness of the title, I am having a hard time even coming up with sort of problem I am facing (if there is a specific name for it....) In a nutshell, I have a time series of points, ...
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119 views

Recovering a distribution after Gaussian noise is added

I have a large dataset (400k rows) in which I suspect the data has been obfuscated by the addition of a Gaussian distribution. My guess is that some of the data had categorical variables (based on the ...
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1answer
59 views

How to use GMMs for acoustic signal classification?

There are a number of applications of the Gaussian Mixture Model (GMMs) to acoustics/audio data for the purposes of classification; ex paper1 and ex paper2. GMMs ...
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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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2answers
459 views

Detection of music note sequence in audio signal

I have an audio signal which contains the combination of different western music notes(I know this combination in advance) and I want to identify the sequence of the music notes present in it. For ...
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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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41 views

Additional Property of Singular Value Decomposition

I am new to SVD so forgive me if the question is trivial. Following is my question. If I have two sets of linear equations, Y1 = T1.X Y2 = T2.X where T1 and T2 are mxn rectangular matrices. Now let'...
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1answer
444 views

Eigenvalue decomposition/SVD and the filtering perspective

I have been studying the SVD algorithm recently and I can understand how it might be used for compression but I am trying to figure out if there is a perspective of SVD where it can be seen as a low ...
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35 views

Estimate Convolution Filter Formula from Noisy Input and Output

When I learned signal processing, I learned how to calculate the output with given input and given convolution filter. However, if now I have the noisy input and output, assuming the system is linear ...
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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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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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36 views

Developing algortihm/model to identify thin linear features in aerial imagery [closed]

I am exploring the possibility of identifying fencelines from NAIP aerial imagery (GSD = 0.6m). I have tried some basic processing in OpenCV using canny edge detection that was detailed in a question ...
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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 ...
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1answer
103 views

Does mutual information capture interactions?

Suppose I have a response $Y$ and two features, $X$ and $Z$. Individually the features are not very predictive but their interaction is strongly predictive. Something like $$Y = 0.5X + 0.5Z + 20XZ + \...
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1answer
116 views

Filtering out bursts with a consistent range from a time series

I have time series of bursts that look like this: … and zoomed in: Now, there are also spurious bursts (which I call noise) in the data, which look like this: … and zoomed in: As you can see, the ...
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26 views

When doing feature selection based on mutual information, should it be normalized?

Are any kind of normalizations useful when using mutual information to select features? The Wikipedia page has a few variants but they don't seem helpful. The entropy of the response is a constant ...
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3answers
423 views

Usage of Hidden Markov Models

I have a set of questions regarding how HMMs are used. Context: there is a stream of real numbers or real number vectors (e.g. data from a phone accelerometer) and the goal is to detect that an ...
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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 ...
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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,...
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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 ...
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2answers
141 views

What features are suitable when predicting user preferences for songs?

I have a data set consisting of 1240 audio files (30 seconds each) and a file like this (two first rows): u v decision 1 323 0 12 9 1 ...
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2answers
230 views

Features for multi-channel time series classification

I am quite confused about extracting features of the multichannel signals and wonder if anyone can help me out. I want to get a feature set where feature is related to time, but I found the only way ...
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0answers
125 views

Is Spearman's rank and RMS error an appropriate measure of similarity between two signals?

I am working on a project comparing the accuracy of two imaging techniques to measure displacement. I have attached a graph comparing the displacement measured by both techniques over time. I am ...
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1answer
662 views

Time Series Classification with Varying Sampling Frequency

I'm new to signal processing and am wondering how to deal with a time-series classification problem when I have unequally spaced data. Skimming through recent literature, including The great time ...
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1answer
360 views

How to combine multiple signal data in my ML model?

I'm doing a task where I need to work with healthcare data from a few different sources. For example, one is an audio signal recording while another is biometric signal reading such as ECG. Both of ...
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48 views

Time alignment of two signal with same length

I have found information about similar topics, but wasn´t useful for me. I have the next 2 signals registered by a laser profilometer. As can be seen in the picture the signals are almost equals but ...
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28 views

Clustering of an image sequence of a moving object

I have a set of 100 images of a man moving on the street. I remove the background and try to cluster the man using dbscan in each image seperately. Instead of getting one cluster (for the man), I get ...