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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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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Breakdown of Music and Esprit Algorithm

MUSIC and ESPRIT are methods that use subspace decomposition to identify signal Parameters. Subspace decomposition is achieved either by SVD or Eigen Value Decomposition. Subspace decomposition ...
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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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132 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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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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156 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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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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377 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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203 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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408 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 ...