The concept of signal decomposition relates to the need to separate one component from the others in a signal; this can be achieved through a filtering operation which require a filter design stage.

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Algorithm for Discrete Signal Decomposition

I am building a sensor and I am trying to understand how to process the signal that it generates. The sensor has a library of reference signals. When 'event a' occurs, it produces signal A, when ...
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Is there R package that combines wavelet and GARCH?

I am new to R but I need to solve a problem related to high frequency data. I need a R package which combines Wavelet and Garch. I found similar approach in MATLAB but not in R.
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what is the difference between EMD and EEMD dealing with HHT?

I have been going through a lot of articles on HHT and EMD. I came across EMD and EEMD. I am not getting a clear picture on the differences between the EMD (Empirical Mode Decomposition) and EEMD ...
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Internal constaint of essential matrix

I work on visual odometry program and I use EmguCV. I use calibrated camera to detect features from current frame with SURF, and match them with previous using Knn. Because I have calibrated camera I ...
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68 views

Decomposition of a signal to slow and fast components

I am currently recording biological responses which are triggered by different events. The figure below shows the original signal (black) and the occurrence of input events (colored dots). There is ...
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81 views

Extracting original signal from overlapping area

Considering this image, where I have a spectral decomposition of a light bulb. Due to the non point shaped light source, the spectral decomposition using a diffraction grating in front of my camera ...
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74 views

What is the right algorithm to detect segmentations of a line chart?

To be concrete, given 2D numerical data as is shown as line plots below. There are peaks on a background average movement (with small vibrations). We want to find the values of pairs (x1, x2) if those ...
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42 views

Decompose an image into better compressible components

Our team develops an application that, in some feature, connects to a scanner (via TWAIN or WIA) and scans a document, and makes a PDF file out of it. The application is mostly used to process mail or ...
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Why is successive decomposition of a signal performed only on low pass component?

The question says it all. In typical (wavelet-like) decomposition of a signal, why is only the low pass component chosen for successive decomposition ?
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What is the difference between Time-Frequency Represenation and TF Decomposition

I'm asking as I'm looking at Wavelet transforms, and I see that it is possible to have a TF decomposition or a representation of the signal. Looking for example at the code here we can see that the ...
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Q and I part in QAM

I have one confusion in QAM about in-phase I and quadrature Q part, i.e. do they transmit identical data or not? For e.g. if i have 11001001 as a byte to be transferred, so will 4-QAM separate it ...
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Suitable metrics for summarizing or visualizing the spatial activation of components after temporal Independent Component Analysis (ICA)

I will first describe the Independent Component Analysis (ICA) steps, so that the question becomes clearer, and more relevant to similar questions. Assume we have $N$ sensors distributed in space. ...
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Optimal filter bank from SVD/PCA

Given a million data points in say 100d, is there a way to generate an optimal filter bank of say 20 filters from an SVD of the data ? Call the 100d space $F$ (as in Frequency), with coordinates ...
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How would I represent an image using a basis $A$, given a sparse or compressible image?

Looking for a Basis representation: Given a sparse or compressible image M, how would one represent this image using a basis A? If I let m = vec(M) m = Ax where A is my "representation" basis and ...
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287 views

Calculating an incoherence property from sub-optimal sampling patterns

EDIT (after comments and subject matter review) CS is based on a choice of a sensing basis $\Phi$ relative to a representation basis $\Psi$. Using an "Incoherence Property" $\mu$ that measures the ...
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339 views

Decomposition of **3D** structuring elements for morphological operations

I am struggling to implement a mathematical morphology toolset in an image processing package. I base my implementation on what I saw in MATLAB, and on several papers on the subject. There seems to ...
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268 views

How do I perform the sifting process in empirical mode decomposition?

I am programming a voice activity detection algorithm and I found a paper that recommends the use of HHT. I have been trying to program it and understand how to calculate $m1(x)$, but the shifting ...
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wavelet transform boundary

I am doing 1D wavelet decomposition and I am particularly interested in parts at the border of the signal. These parts are affected by boundary effects. I know that some of the methods to extend the ...
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81 views

Can Cholesky outer product version result in negative square roots?

Say A is symmetric positive definite matrix , which means one necessary condition is diagonal entries of A are positive. If I do cholesky factorisation using outer product form, Can there be any ...
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I and Q Channels

My understanding of I and Q channels is as follows (please correct me if I am wrong): I = In-phase, or real component Q = ...
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497 views

Time-frequency analysis of non-sinusoidal periodic signals

Given the history of the sum of a time-varying mixture of periodic signals, say square waves, how would you efficiently estimate the number and frequencies of components active at a particular time? ...
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236 views

Empirical Mode Decomposition and Sparsity

In what sense does empirical mode decomposition (EMD) bring out the sparsity in a signal? For instance, if I had a signal $f$ and I broke it down into $n$ intrinsic mode functions (IMF), what should ...
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568 views

Mathematics / Signal theory behind billiard ball 'wave pendulum' effect

This YouTube video shows a very interesting effect. What is the underlying science? I have recently started studying Fourier theory and DSP, and and trying to understand what is going on in terms of ...